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Global Well-Posedness of the Fractional Tropical Climate Model
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作者 Meiqi Hu 《Journal of Applied Mathematics and Physics》 2024年第3期805-818,共14页
In this paper, we consider the Cauchy problem of 3-dimensional tropical climate model. This model reflects the interaction and coupling among the barotropic mode u, the first baroclinic mode v of the velocity and the ... In this paper, we consider the Cauchy problem of 3-dimensional tropical climate model. This model reflects the interaction and coupling among the barotropic mode u, the first baroclinic mode v of the velocity and the temperature θ. The systems with fractional dissipation studied here may arise in the modeling of geophysical circumstances. Mathematically these systems allow simultaneous examination of a family of systems with various levels of regularization. The aim here is the global strong solution with the least dissipation. By energy estimate and delicate analysis, we prove the existence of global solution under three different cases: first, with the help of damping terms, the global strong solution of the system with Λ<sup>2a</sup>u, Λ<sup>2β</sup>v and Λ<sup>2γ</sup> θ for;and second, the global strong solution of the system for with damping terms;finally, the global strong solution of the system for without any damping terms, which improve the known existence theory for this system. 展开更多
关键词 Tropical Climate Model Fractional Diffusion global Existence
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ALMOST SURE GLOBAL WELL-POSEDNESS FOR THE FOURTH-ORDER NONLINEAR SCHR?DINGER EQUATION WITH LARGE INITIAL DATA
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作者 陈明娟 张帅 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期2215-2233,共19页
We consider the fourth-order nonlinear Schr?dinger equation(4NLS)(i?t+εΔ+Δ2)u=c1um+c2(?u)um-1+c3(?u)2um-2,and establish the conditional almost sure global well-posedness for random initial data in Hs(Rd)for s∈(sc-... We consider the fourth-order nonlinear Schr?dinger equation(4NLS)(i?t+εΔ+Δ2)u=c1um+c2(?u)um-1+c3(?u)2um-2,and establish the conditional almost sure global well-posedness for random initial data in Hs(Rd)for s∈(sc-1/2,sc],when d≥3 and m≥5,where sc:=d/2-2/(m-1)is the scaling critical regularity of 4NLS with the second order derivative nonlinearities.Our proof relies on the nonlinear estimates in a new M-norm and the stability theory in the probabilistic setting.Similar supercritical global well-posedness results also hold for d=2,m≥4 and d≥3,3≤m<5. 展开更多
关键词 fourth-order Schrodinger equation random initial data almost sure global well-posedness M-norm stability theory
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GLOBAL WELL-POSEDNESS AND OPTIMAL TIME DECAY RATES FOR THE GENERALIZED PHAN-THIEN-TANNER MODEL IN R^(3)
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作者 陈玉惠 姚清河 +1 位作者 李敏玲 姚正安 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1301-1322,共22页
In this paper, we consider the initial value problem for the incompressible generalized Phan-Thien-Tanner(GPTT) model. This model pertains to the dynamic properties of polymeric fluids. Under appropriate assumptions o... In this paper, we consider the initial value problem for the incompressible generalized Phan-Thien-Tanner(GPTT) model. This model pertains to the dynamic properties of polymeric fluids. Under appropriate assumptions on smooth function f, we find a particular solution to the GPTT model. In dimension three, we establish the global existence and the optimal time decay rates of strong solutions provided that the initial data is close to the particular solution. The results which are presented here are generalizations of the network viscoelastic models. 展开更多
关键词 viscoelastic fluids global well-posedness decay rates
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GLOBAL WELL-POSEDNESS OF THE STOCHASTIC 2D BOUSSINESQ EQUATIONS WITH PARTIAL VISCOSITY 被引量:3
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作者 蒲学科 郭柏灵 《Acta Mathematica Scientia》 SCIE CSCD 2011年第5期1968-1984,共17页
This paper deals with the stochastic 2D Boussinesq equations with partial viscosity. This is a coupled system of Navier-Stokes/Euler equations and the transport equation for temperature under additive noise. Global we... This paper deals with the stochastic 2D Boussinesq equations with partial viscosity. This is a coupled system of Navier-Stokes/Euler equations and the transport equation for temperature under additive noise. Global well-posedness result of this system under partial viscosity is proved by using classical energy estimates method. 展开更多
关键词 stochastic PDEs Boussinesq equations global well-posedness
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GLOBAL WELL-POSEDNESS OF THE 2D INCOMPRESSIBLE MICROPOLAR FLUID FLOWS WITH PARTIAL VISCOSITY AND ANGULAR VISCOSITY 被引量:2
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作者 陈明涛 《Acta Mathematica Scientia》 SCIE CSCD 2013年第4期929-935,共7页
This paper is concerned with the two-dimensional equations of incompress- ible micropolar fluid flows with mixed partial viscosity and angular viscosity. The global existence and uniqueness of smooth solution to the C... This paper is concerned with the two-dimensional equations of incompress- ible micropolar fluid flows with mixed partial viscosity and angular viscosity. The global existence and uniqueness of smooth solution to the Cauchy problem is established. 展开更多
关键词 micropolar fluid global well-posedness partial viscosities
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GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES 被引量:2
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作者 Muhammad Zainul ABIDIN Jiecheng CHEN 《Acta Mathematica Scientia》 SCIE CSCD 2021年第1期164-176,共13页
In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space F N^(s(·))p(·),h(·),q(R^(3))with s(·)=4-2... In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space F N^(s(·))p(·),h(·),q(R^(3))with s(·)=4-2α-3/p(·).We prove global well-posedness result with small initial data belonging to FN^(4-2α-3/p(·))p(·),h(·)q(R^(3)).The result of this paper extends some recent work. 展开更多
关键词 fractional Navier-Stokes equations global well-posedness Fourier-Besov-Morrey space
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Global Well-posedness of the Generalized Long-short Wave Equations 被引量:2
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作者 ZHANG Rui-feng LIANG Hong-wei 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第4期538-544,共7页
In the present paper, we investigate the well-posedness of the global solutionfor the Cauchy problem of generalized long-short wave equations. Applying Kato's methodfor abstract quasi-linear evolution equations and a... In the present paper, we investigate the well-posedness of the global solutionfor the Cauchy problem of generalized long-short wave equations. Applying Kato's methodfor abstract quasi-linear evolution equations and a priori estimates of solution,we get theexistence of globally smooth solution. 展开更多
关键词 the generalized long-short wave equations Kato's method uniformly a prioriestimate global well-posedness
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GLOBAL WELL-POSEDNESS FOR A FIFTH-ORDER SHALLOW WATER EQUATION ON THE CIRCLE 被引量:1
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作者 李用声 杨兴雨 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1303-1317,共15页
The periodic initial value problem of a fifth-order shallow water equation t u 2 x t u + 3 x u 5 x u + 3u x u 2 x u 2 x u u 3 x u = 0 is shown to be globally well-posed in Sobolev spaces˙ H s (T) for s 〉 2/3 by ... The periodic initial value problem of a fifth-order shallow water equation t u 2 x t u + 3 x u 5 x u + 3u x u 2 x u 2 x u u 3 x u = 0 is shown to be globally well-posed in Sobolev spaces˙ H s (T) for s 〉 2/3 by I-method. For this equation lacks scaling invariance, we first reconsider the local result and pay special attention to the relationship between the lifespan of the local solution and the initial data, and then prove the almost conservation law, and finally obtain the global well-posedness by an iteration process. 展开更多
关键词 shallow water equation periodic initial value problem global well-posedness I-METHOD almost conservation law
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GLOBAL WELL-POSEDNESS OF THE 2D BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION 被引量:1
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作者 Xueting Jin Yuelong Xiao Huan Yu 《Acta Mathematica Scientia》 SCIE CSCD 2022年第4期1293-1309,共17页
In this paper,we prove the global well-posedness of the 2 D Boussinesq equations with three kinds of partial dissipation;among these the initial data(u_(0),θ_(0))is required such that its own and the derivative of on... In this paper,we prove the global well-posedness of the 2 D Boussinesq equations with three kinds of partial dissipation;among these the initial data(u_(0),θ_(0))is required such that its own and the derivative of one of its directions(x,y)are assumed to be L^(2)(R^(2)).Our results only need the lower regularity of the initial data,which ensures the uniqueness of the solutions. 展开更多
关键词 Two-dimensional Boussinesq equations global well-posedness partial dissipation and diffusion
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GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE MASS-CRITICAL HARTREE EQUATION IN HIGH DIMENSIONS
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作者 夏红强 《Acta Mathematica Scientia》 SCIE CSCD 2015年第1期255-274,共20页
We obtain global well-posedness and scattering, and global L2(d+2)/d t,x spacetime bounds for solutions to the defocusing mass-critical Hartree equation in Rt×Rx^d,d≥5.
关键词 Haxtree equation global well-posedness SCATTERING mass-critical
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GLOBAL WELL-POSEDNESSOF A PRANDTL MODEL FROM MHD IN GEVREY FUNCTION SPACES
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作者 Weixi LI Rui XU Tong YANG 《Acta Mathematica Scientia》 SCIE CSCD 2022年第6期2343-2366,共24页
We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer.A global-in-time well-posedness is obtained in the Gevrey function s... We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer.A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index 2.The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator. 展开更多
关键词 magnetic Prandtl equation Gevrey function space global well-posedness auxiliaryfunctions loss of derivative
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GLOBAL WELL-POSEDNESS FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS
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作者 Jinlu LI Zhaoyang YIN Xiaoping ZHAI 《Acta Mathematica Scientia》 SCIE CSCD 2022年第5期2131-2148,共18页
We are concerned with the Cauchy problem regarding the full compressible Navier-Stokes equations in R^(d)(d=2,3).By exploiting the intrinsic structure of the equations and using harmonic analysis tools(especially the ... We are concerned with the Cauchy problem regarding the full compressible Navier-Stokes equations in R^(d)(d=2,3).By exploiting the intrinsic structure of the equations and using harmonic analysis tools(especially the Littlewood-Paley theory),we prove the global solutions to this system with small initial data restricted in the Sobolev spaces.Moreover,the initial temperature may vanish at infinity. 展开更多
关键词 compressible Navier-Stokes equations global well-posedness Friedrich's method compactness arguments
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GLOBAL WELL-POSEDNESS IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION
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作者 霍朝辉 《Acta Mathematica Scientia》 SCIE CSCD 2016年第4期1117-1152,共36页
The Cauchy problem of the Klein-Gordon-Zakharov equation in three dimensional space is considered. It is shown that it is globally well-posed in energy space H^1 × L^2 × L^2 ×... The Cauchy problem of the Klein-Gordon-Zakharov equation in three dimensional space is considered. It is shown that it is globally well-posed in energy space H^1 × L^2 × L^2 × H^-1 if small initial data (u0 (x), u1 (x), n0 (x), n1 (x)) ∈ (H^1 ×L^2× L^2 × H^-1). It answers an open problem: Is it globally well-posed in energy space H^1 × L^2 × L^2 × H^-1 for 3D Klein-Gordon- Zakharov equation with small initial data [1, 2]? The method in this article combines the linear property of the equation ( dispersive property) with nonlinear property of the equation (energy inequalities). We mainly extend the spaces F^s and N^3 in one dimension [3] to higher dimension. 展开更多
关键词 global well-posedness 3D Klein-Gordon-Zakharov equation dyadic Xs b spacesin higher dimension
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A NOTE ON GLOBAL WELL-POSEDNESS OF SOLUTIONS TO BOUSSINESQ EQUATIONS WITH FRACTIONAL DISSIPATION 被引量:6
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作者 叶专 《Acta Mathematica Scientia》 SCIE CSCD 2015年第1期112-120,共9页
The goal of this paper is to consider the global well-posedness to n-dimensional (n 〉 3) Boussinesq equations with fractional dissipation. More precisely, it is proved that there exists a unique global regular solu... The goal of this paper is to consider the global well-posedness to n-dimensional (n 〉 3) Boussinesq equations with fractional dissipation. More precisely, it is proved that there exists a unique global regular solution to the Boussinesq equations provided the real parameter α satisfies α≥1/2 +n/4. 展开更多
关键词 Boussinesq equations fractional Laplacian global regularity
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GLOBAL WELL-POSEDNESS FOR THE DENSITY-DEPENDENT INCOMPRESSIBLE MAGNETOHYDRODYNAMIC FLOWS IN BOUNDED DOMAINS 被引量:1
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作者 Defu CHEN Xia YE. 《Acta Mathematica Scientia》 SCIE CSCD 2018年第6期1833-1845,共13页
In this paper, we study the three-dimensional incompressible magnetohydrody-namic equations in a smooth bounded domains, in which the viscosity of the fluid and themagnetic diffusivity are concerned with density. The ... In this paper, we study the three-dimensional incompressible magnetohydrody-namic equations in a smooth bounded domains, in which the viscosity of the fluid and themagnetic diffusivity are concerned with density. The existence of global strong solutions isestablished in vacuum cases, provided the assumption that (| |μ(ρ0)||Lp+|| v(P0)||Lq+||b0||L^3 +||ρO||L^∞) (p,q〉3) is small enough, there is not any smallness condition on thevelocity. 展开更多
关键词 incompressible MHD global solution small initial data
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Global well-posedness for 2D inhomogeneous asymmetric fluids with large initial data
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作者 Chenyin Qian Beibei He Ting Zhang 《Science China Mathematics》 SCIE CSCD 2024年第3期527-556,共30页
In this paper, by using time-weighted global estimates and the Lagrangian approach, we first investigate the global existence and uniqueness of the solution for the 2D inhomogeneous incompressible asymmetric fluids wi... In this paper, by using time-weighted global estimates and the Lagrangian approach, we first investigate the global existence and uniqueness of the solution for the 2D inhomogeneous incompressible asymmetric fluids with the initial(angular) velocity being located in sub-critical Sobolev spaces H^(s)(R^(2))(0<s<1) and the initial density being bounded from above and below by some positive constants. The global unique solvability of the 2D incompressible inhomogeneous asymmetric fluids with the initial data in the critical Besov space(u_(0), w_(0))∈˙B^(0)_(2,1)(R^(2))andρ^(−1)−1∈˙B^(ε)_(2/ε),1(R^(2))is established. In particular, the uniqueness of the solution is also obtained without any more regularity assumptions on the initial density which is an improvement on the recent result of Abidi and Gui(2021) for the 2D inhomogeneous incompressible NavierStokes system. 展开更多
关键词 inhomogeneous asymmetric fluids Littlewood-Paley theory Besov spaces global well-posedness
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Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces
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作者 AZANZAL Achraf ALLALOU Chakir +1 位作者 MELLIANI Said ABBASSI Adil 《Journal of Partial Differential Equations》 CSCD 2023年第1期1-21,共21页
In this paper,we study the subcritical dissipative quasi-geostrophic equa-tion.By using the Littlewood Paley theory,Fourier analysis and standard techniques we prove that there exists a unique global-in-time solution ... In this paper,we study the subcritical dissipative quasi-geostrophic equa-tion.By using the Littlewood Paley theory,Fourier analysis and standard techniques we prove that there exists a unique global-in-time solution for small initial data belonging to the critical Fourier-Besov-Morrey spaces FN^(3-2a+(λ-2)/p)_(p,λ,q).Moreover,we show the asymptotic behavior of the global solution v.i.e.||v(t)||FN^(3-2a+(λ-2)/p)_(p,λ,q)decays to zero as time goes to infinity. 展开更多
关键词 2D quasi-geostrophic equation subcritical dissipation Littlewood-Paley theory global well-posedness long time behavior of the solution Fourier-Besov-Morrey spaces
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Global well-posedness of the MHD equations via the comparison principle 被引量:3
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作者 Dongyi Wei Zhifei Zhang 《Science China Mathematics》 SCIE CSCD 2018年第11期2111-2120,共10页
In this paper,we prove the global well-posedness of the incompressible magneto-hydrodynamics(MHD)equations near a homogeneous equilibrium in the domain R^k×T^(d-k),d≥2,k≥1 by using the comparison principle and ... In this paper,we prove the global well-posedness of the incompressible magneto-hydrodynamics(MHD)equations near a homogeneous equilibrium in the domain R^k×T^(d-k),d≥2,k≥1 by using the comparison principle and constructing the comparison function. 展开更多
关键词 MHD equations comparison principle global well-posedness
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Global well-posedness for the 3-D MHD equations with partial diffusion in the periodic domain 被引量:2
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作者 Wenji Chen Zhifei Zhang Jianfeng Zhou 《Science China Mathematics》 SCIE CSCD 2022年第2期309-318,共10页
In this paper, we prove the global well-posedness of the 3-D magnetohydrodynamics(MHD) equations with partial diffusion in the periodic domain when the initial velocity is small and the initial magnetic field is close... In this paper, we prove the global well-posedness of the 3-D magnetohydrodynamics(MHD) equations with partial diffusion in the periodic domain when the initial velocity is small and the initial magnetic field is close to a background magnetic field satisfying the Diophantine condition. 展开更多
关键词 MHD equations global well-posedness Diophantine condition
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Lagrangian Approach to Global Well-Posedness of the Viscous Surface Wave Equations Without Surface Tension 被引量:2
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作者 Guilong Gui 《Peking Mathematical Journal》 2021年第1期1-82,共82页
In this paper,we revisit the global well-posedness of the classical viscous surface waves in the absence of surface tension effect with the reference domain being the horizontal infinite slab,for which the first compl... In this paper,we revisit the global well-posedness of the classical viscous surface waves in the absence of surface tension effect with the reference domain being the horizontal infinite slab,for which the first complete proof was given in Guo-Tice[Anal.PDE 6,1429-1533(2013)]via a hybrid of Eulerian and Lagrangian schemes.The fluid dynamics are governed by the gravity-driven incompressible Navier-Stokes equations.Even though Lagrangian formulation is most natural to study free boundary value problems for incompressible flows,few mathematical works for global existence are based on such an approach in the absence of surface ten-sion effect,due to breakdown of Beale’s transformation.We develop a mathematical approach to establish global well-posedness based on the Lagrangian framework by analyzing suitable“good unknowns”associated with the problem,which requires no nonlinear compatibility conditions on the initial data. 展开更多
关键词 Viscous surface waves Lagrangian coordinates global well-posedness
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