By extending the concept of asymptotic weakly Pareto-Nash equilibrium point to vector-valued case, Tikhonov well-posedness and Hadamard well-posedness results of the multiobjective generalized games are established in...By extending the concept of asymptotic weakly Pareto-Nash equilibrium point to vector-valued case, Tikhonov well-posedness and Hadamard well-posedness results of the multiobjective generalized games are established in this paper.展开更多
The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects （like particle tunnelling through potential barriers and built-up...The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects （like particle tunnelling through potential barriers and built-up in quantum wells） take place, is considered in the present paper, and the recent progress on well-posedness, stability analysis, and small scaling limits are reviewed.展开更多
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
In this paper we prove local well-posedness in critical Besov spaces for the full compressible MHD equations in R^N, N≥ 2, under the assumptions that the initialdensity is bounded away from zero. The proof relies on ...In this paper we prove local well-posedness in critical Besov spaces for the full compressible MHD equations in R^N, N≥ 2, under the assumptions that the initialdensity is bounded away from zero. The proof relies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.展开更多
In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are...In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given.展开更多
In this paper,we recall the Stokes coupling method for solving the exteriorunsteady Navier-Stokes equations.Moreover, we derive the coupling variational formulation of the Stokes coupling problem by use of the integra...In this paper,we recall the Stokes coupling method for solving the exteriorunsteady Navier-Stokes equations.Moreover, we derive the coupling variational formulation of the Stokes coupling problem by use of the integral representations of the solntion of the Stokes equations at an infinite domain.Finain Finally, we provide some properties of the integral operators over the articleal boundary and the well-posedness of the coupling variational formulation.展开更多
A systematic study was made on the topological nature of the system of non-static rotating fluid. Several initial (boundary) value problems and their well-posedness were discussed.
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
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
In this paper, some theoretical notions of well-posedness and of well-posedness in the generalized sense for scalar optimization problems are presented and some important results are analysed. Similar notions of well-...In this paper, some theoretical notions of well-posedness and of well-posedness in the generalized sense for scalar optimization problems are presented and some important results are analysed. Similar notions of well-posedness, respectively for a vector optimization problem and for a variational inequality of differential type, are discussed subsequently and, among the various vector well-posedness notions known in the literature, the attention is focused on the concept of pointwise well-posedness. Moreover, after a review of well-posedness properties, the study is further extended to a scalarizing procedure that preserves well-posedness of the notions listed, namely to a result, obtained with a special scalarizing function, which links the notion of pontwise well-posedness to the well-posedness of a suitable scalar variational inequality of differential type.展开更多
We investigate the solution of an N-unit series system with finite number of vacations. By using C0-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic soluti...We investigate the solution of an N-unit series system with finite number of vacations. By using C0-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.展开更多
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.
This paper is concerned with the Cauchy problem of a seventh order dispersive equation. We prove local well-posedness with initial data in Sobolev spaces Hs（R） for negative indices of s〉-114 .
The well-posedness of the initial value problem of the Euler equations was mainly discussed based on the stratification theory, and the necessary and sufficient conditions of well-posedness are presented for some repr...The well-posedness of the initial value problem of the Euler equations was mainly discussed based on the stratification theory, and the necessary and sufficient conditions of well-posedness are presented for some representative initial or boundary value problem, thus the structure of solution space for local （exact） solution of the Euler equations is determined. Moreover the computation formulas of the analytical solution of the well-posed problem are also given.展开更多
This current paper is devoted to the Cauchy problem for higher order dispersive equation ut＋δx^2n＋1u=δx（uδx^nu）＋δx^n-1（ux^2）, n ≥ 2, n ∈ N^＋. Ut By using Besov-type spaces, we prove that the associated ...This current paper is devoted to the Cauchy problem for higher order dispersive equation ut＋δx^2n＋1u=δx（uδx^nu）＋δx^n-1（ux^2）, n ≥ 2, n ∈ N^＋. Ut By using Besov-type spaces, we prove that the associated problem is locally well-posed in H（-n/2＋3/4,-1/2n）. The new ingredient is that we establish some new dyadic bilinear estimates. When n is even, we also prove that the associated equation is ill-posed in H^（s,a）（R） with s〈-n/2＋3/4 and all a∈R.展开更多
The initial boundary value problem of the one-dimensional magneto-hydrodynamics system, when the viscosity, thermal conductivity, and magnetic diffusion coefficients are general smooth functions of temperature, is con...The initial boundary value problem of the one-dimensional magneto-hydrodynamics system, when the viscosity, thermal conductivity, and magnetic diffusion coefficients are general smooth functions of temperature, is considered in this article. A unique global classical solution is shown to exist uniquely and converge to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent γ. The initial data can be large if γ is sufficiently close to 1.展开更多
The influence of the random perturbations on the fourth-order nonlinear SchrSdinger equations,iut＋△^2u＋ε△u＋λ｜u｜^p-1u=ξ,（t,x）∈R^＋×R^n,n≥1,ε∈{-1,0,＋1},is investigated in this paper. The local well...The influence of the random perturbations on the fourth-order nonlinear SchrSdinger equations,iut＋△^2u＋ε△u＋λ｜u｜^p-1u=ξ,（t,x）∈R^＋×R^n,n≥1,ε∈{-1,0,＋1},is investigated in this paper. The local well-posedness in the energy space H^2（R^n） are proved for p 〉n＋4/n＋2,and p≤2^#-1 if n≥5.Global existence is also derived for either defocusing or focusing L^2-subcritical nonlinearities.展开更多
The well-posedness of the initial-boundary value problem of the time-varying linear electromagnetic field in a multi-medium region is investigated. Function spaces are defined, with Faraday＇s law of electromagnetic i...The well-posedness of the initial-boundary value problem of the time-varying linear electromagnetic field in a multi-medium region is investigated. Function spaces are defined, with Faraday＇s law of electromagnetic induction and the initial-boundary conditions considered as constraints. Gauss＇s formula applied to a multi-medium region is used to derive the energy-estimating inequality. After converting the initial-boundary conditions into homogeneous ones and analysing the characteristics of an operator introduced according to the total current law, the existence, uniqueness and stability of the weak solution to the initial-boundary value problem of the time-varying linear electromagnetic field are proved.展开更多
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
基金Supported by Natural Science Foundation of Guizhou Province
文摘By extending the concept of asymptotic weakly Pareto-Nash equilibrium point to vector-valued case, Tikhonov well-posedness and Hadamard well-posedness results of the multiobjective generalized games are established in this paper.
基金L.H. is supported in part by the NSFC (10431060) H.L. is supported partially by the NSFC (10431060, 10871134)+1 种基金the Beijing Nova program (2005B48)the NCET support of the Ministry of Education of China, and the Huo Ying Dong Foundation (111033)
文摘The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects （like particle tunnelling through potential barriers and built-up in quantum wells） take place, is considered in the present paper, and the recent progress on well-posedness, stability analysis, and small scaling limits are reviewed.
文摘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.
文摘In this paper we prove local well-posedness in critical Besov spaces for the full compressible MHD equations in R^N, N≥ 2, under the assumptions that the initialdensity is bounded away from zero. The proof relies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.
基金supported by the National Science Foundation of China and Shanghai Pujian Program
文摘In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given.
文摘In this paper,we recall the Stokes coupling method for solving the exteriorunsteady Navier-Stokes equations.Moreover, we derive the coupling variational formulation of the Stokes coupling problem by use of the integral representations of the solntion of the Stokes equations at an infinite domain.Finain Finally, we provide some properties of the integral operators over the articleal boundary and the well-posedness of the coupling variational formulation.
文摘A systematic study was made on the topological nature of the system of non-static rotating fluid. Several initial (boundary) value problems and their well-posedness were discussed.
文摘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.
基金supported by NSFC (10771074)NSFC-NSAF(10976026)+1 种基金Yang was partially supported by NSFC (10801055 10901057)
文摘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.
文摘In this paper, some theoretical notions of well-posedness and of well-posedness in the generalized sense for scalar optimization problems are presented and some important results are analysed. Similar notions of well-posedness, respectively for a vector optimization problem and for a variational inequality of differential type, are discussed subsequently and, among the various vector well-posedness notions known in the literature, the attention is focused on the concept of pointwise well-posedness. Moreover, after a review of well-posedness properties, the study is further extended to a scalarizing procedure that preserves well-posedness of the notions listed, namely to a result, obtained with a special scalarizing function, which links the notion of pontwise well-posedness to the well-posedness of a suitable scalar variational inequality of differential type.
文摘We investigate the solution of an N-unit series system with finite number of vacations. By using C0-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.
文摘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.
基金supported by the National Natural Science Foundation of China(11171266)
文摘This paper is concerned with the Cauchy problem of a seventh order dispersive equation. We prove local well-posedness with initial data in Sobolev spaces Hs（R） for negative indices of s〉-114 .
文摘The well-posedness of the initial value problem of the Euler equations was mainly discussed based on the stratification theory, and the necessary and sufficient conditions of well-posedness are presented for some representative initial or boundary value problem, thus the structure of solution space for local （exact） solution of the Euler equations is determined. Moreover the computation formulas of the analytical solution of the well-posed problem are also given.
基金supported by Natural Science Foundation of China NSFC(11401180 and 11471330)supported by the Young Core Teachers Program of Henan Normal University(15A110033)supported by the Fundamental Research Funds for the Central Universities(WUT:2017 IVA 075)
文摘This current paper is devoted to the Cauchy problem for higher order dispersive equation ut＋δx^2n＋1u=δx（uδx^nu）＋δx^n-1（ux^2）, n ≥ 2, n ∈ N^＋. Ut By using Besov-type spaces, we prove that the associated problem is locally well-posed in H（-n/2＋3/4,-1/2n）. The new ingredient is that we establish some new dyadic bilinear estimates. When n is even, we also prove that the associated equation is ill-posed in H^（s,a）（R） with s〈-n/2＋3/4 and all a∈R.
基金Supported by NNSFC(11271306)the Natural Science Foundation of Fujian Province of China(2015J01023)the Fundamental Research Funds for the Central Universities of Xiamen University(20720160012)
文摘The initial boundary value problem of the one-dimensional magneto-hydrodynamics system, when the viscosity, thermal conductivity, and magnetic diffusion coefficients are general smooth functions of temperature, is considered in this article. A unique global classical solution is shown to exist uniquely and converge to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent γ. The initial data can be large if γ is sufficiently close to 1.
基金Supported by NSFC (10871175,10931007,10901137)Zhejiang Provincial Natural Science Foundation of China (Z6100217)SRFDP (20090101120005)
文摘The influence of the random perturbations on the fourth-order nonlinear SchrSdinger equations,iut＋△^2u＋ε△u＋λ｜u｜^p-1u=ξ,（t,x）∈R^＋×R^n,n≥1,ε∈{-1,0,＋1},is investigated in this paper. The local well-posedness in the energy space H^2（R^n） are proved for p 〉n＋4/n＋2,and p≤2^#-1 if n≥5.Global existence is also derived for either defocusing or focusing L^2-subcritical nonlinearities.
基金Project supported by the National Natural Science Foundation of China （Grant No 50377002）.
文摘The well-posedness of the initial-boundary value problem of the time-varying linear electromagnetic field in a multi-medium region is investigated. Function spaces are defined, with Faraday＇s law of electromagnetic induction and the initial-boundary conditions considered as constraints. Gauss＇s formula applied to a multi-medium region is used to derive the energy-estimating inequality. After converting the initial-boundary conditions into homogeneous ones and analysing the characteristics of an operator introduced according to the total current law, the existence, uniqueness and stability of the weak solution to the initial-boundary value problem of the time-varying linear electromagnetic field are proved.
文摘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.
