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THE IMPROVED FOURIER SPLITTING METHOD AND DECAY ESTIMATES OF THE GLOBAL SOLUTIONS OF THE CAUCHY PROBLEMS FOR NONLINEAR SYSTEMS OF FLUID DYNAMICS EQUATIONS
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作者 Linghai Zhang 《Annals of Applied Mathematics》 2016年第4期396-417,共22页
Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp ra... Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple togeth- er the elementary uniform energy estimates of the global weak solutions and a well known Gronwall's inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980's to study the op- timal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay esti- mates with sharp rates of the global weak solutions of the Cauchy problems for n-dimensional incompressible Navier-Stokes equations, for the n-dimensional magnetohydrodynamics equations and for many other very interesting nonlin- ear evolution equations with dissipations can be established. 展开更多
关键词 nonlinear systems of fluid dynamics equations global weaksolutions decay estimates uniform energy estimates fourier transformation Plancherel's identity Gronwall's inequality improved fourier splitting method
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Lower Bounds of Decay Rates for Solution to the Single-Layer Quasi-Geostrophic Model
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作者 Haoyu Zhao 《Journal of Applied Mathematics and Physics》 2023年第8期2221-2230,共10页
In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizi... In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies . 展开更多
关键词 Single-Layer Quasi-Geostrophic Model Lower Bounds fourier splitting method
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Well-Posedness and Decay of Solution to Three-Dimensional Generalized Navier-Stokes Equations with Damping
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作者 LIU Xiaofeng ZOU Lulu 《Journal of Donghua University(English Edition)》 EI CAS 2020年第5期396-401,共6页
The generalized Navier-Stokes equations with damping are considered.We will show that the generalized Navier-Stokes equations with damping |u|^β-1u have weak solutions for anyβ>1 and 0<α<5/4,and we will us... The generalized Navier-Stokes equations with damping are considered.We will show that the generalized Navier-Stokes equations with damping |u|^β-1u have weak solutions for anyβ>1 and 0<α<5/4,and we will use the Fourier splitting method to prove the L2 decay of weak solutions forβ>2 and 0<α<3/4. 展开更多
关键词 generalized Navier-Stokes equation DAMPING DECAY fourier splitting method
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A Remark on the Time Decay of Non-Newtonian Flows in R3
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作者 YIN Gu-liang 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第1期69-74,共6页
In the study of long time asymptotic behaviors of the solutions to a class system of the incompressible non-Newtonian fluid flows in R3, it is proved that the weak solutions decay in L2 norm at (1 + t)- 3/4 and the... In the study of long time asymptotic behaviors of the solutions to a class system of the incompressible non-Newtonian fluid flows in R3, it is proved that the weak solutions decay in L2 norm at (1 + t)- 3/4 and the error of difference between non-Newtonian fluid and linear equation is also investigated. The findings are mainly based on the classic Fourier splitting methods. 展开更多
关键词 decay rates fourier splitting methods non-Newtonian flows
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Upper Bounds of the Rates of Decay for Solutions of the Boussinesq Equations
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作者 Ying Liu 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2011年第1期105-114,共10页
In this paper, upper bounds of the L2-decay rate for the Boussinesq equations are considered. Using the L2 decay rate of solutions for the heat equation, and assuming that the solutions of the Boussinesq equations are... In this paper, upper bounds of the L2-decay rate for the Boussinesq equations are considered. Using the L2 decay rate of solutions for the heat equation, and assuming that the solutions of the Boussinesq equations are smooth, we obtain the upper bounds of L2 decay rate for the smooth solutions and difference between the solutions of the Boussinesq equations and those of the heat system with the same initial data. The decay results may then be obtained by passing to the limit of approximating sequences of solutions. The main tool is the Fourier splitting method. 展开更多
关键词 the Boussinesq equations L2 decay fourier splitting method
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Large Time Behavior of Solutions to the Generalized Hall-Magnetohydrodynamics System
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作者 FANG Hui BIE Qunyi 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2021年第4期299-304,共6页
In this paper,we investigate the large time behavior of solutions to the three dimensional generalized Hall-magnetohydrodynamics(Hall-MHD)system in the spacesχ^(s)(R^(3)).We obtain that the temporal decay rate is‖(u... In this paper,we investigate the large time behavior of solutions to the three dimensional generalized Hall-magnetohydrodynamics(Hall-MHD)system in the spacesχ^(s)(R^(3)).We obtain that the temporal decay rate is‖(u,b)(t)‖χ^(1−2α)+‖(u,b)(t)‖χ^(1−2β)+‖(u,b)(t)‖χ^(2−2α)+‖(u,b)(t)‖χ^(2−2β)≤(1 t)^(-(5-4max{α,β}/4max{α,β})with 1/2≤α,β≤1 for the small global solution by using Fourier splitting method.The parametersαandβare the fractional dissipations corresponding to the velocity and magnetic field,respectively. 展开更多
关键词 generalized Hall-magnetohydrodynamics(Hall-MHD)system large time behavior fourier splitting method
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