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large-time behavior of Periodic Solutions to Fractal Burgers Equation with large Initial Data

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Chinese Annals of Mathematics,Series B 2012年第3期33卷 405-418页

作者： Lijuan WANG Weike WANG Department of Mathematics Shanghai Jiao Tong UniversityShanghai 200240China

The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily *** exponential decay estimates of the solutions are obtained for th... 详细信息

关键词： Fractal Burgers equation large-time behavior large initial data Periodic solution Exponential decay

large-time behavior of Solutions to the Stokes Approximation Equations for Two Dimensional Compressible Flows

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Acta Mathematicae Applicatae Sinica 2005年第4期21卷 637-654页

作者： Zhen-hua Guo Department of Mathematics and Statistics Huazhong Normal University Wuhan 430079 China LCP Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China

In this paper, we study the large time asymptotic behavior of solutions to both the Cauchy problem and the exterior problem of the Stokes approximation equations of two dimensional compressible flows.

关键词： large-time behavior Stokes approximation equations two dimension

Global existence and large-time behavior for primitive equations with the free boundary

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Science China Mathematics 2024年第10期67卷 2303-2330页

作者： Hai-Liang Li Chuangchuang Liang School of Mathematical Sciences Capital Normal UniversityBeijing 100048China Academy for Multidisciplinary Studies Capital Normal UniversityBeijing 100048China College of Mathematics and Statistics Chongqing UniversityChongqing 401331China

In the present paper, the primitive equations, which can be used to simulate the large-scale motion of the ocean and atmosphere, are considered in the three-dimensional domain bounded below by a fixed solid boundary and above by a free-moving boundary. The global existence and uniqueness of strong solutions are established, and the long-time convergence to the equilibrium state is shown to be either at an exponential rate for the horizontal periodic domain or at an algebraic rate for the horizontal whole space.

关键词： primitive equations the free boundary value problem global well-posedness large-time behavior

Global Strong Solutions and large-time behavior of 2D Tropical Climate Model

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Acta Mathematicae Applicatae Sinica 2023年第4期39卷 886-925页

作者： Dong-juan NIU Ying WANG School of Mathematical Sciences Capital Normal UniversityBeijing 100048China School of Physical Science and Technology Guangxi UniversityNanning 530004China

In this paper we mainly deal with the global well-posedness and large-time behavior of the 2D tropical climate model with small initial data. We first establish the global well-posedness of solution in the Besov space, then we obtain the optimal decay rates of solutions by virtue of the frequency decomposition method. Specifically, for the low frequency part, we use the Fourier splitting method of Schonbek and the spectrum analysis method, and for the high frequency part, we use the global energy estimate and the behavior of exponentially decay operator.

关键词： tropical climate model large-time behavior global well-posedness

ASYMPTOTIC behavior OF SOLUTIONS TO THE COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA WITH BOUNDARY EFFECTS

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Chinese Annals of Mathematics,Series B 2002年第1期23卷 109-118页

作者： HSIAOLING LIHAILIANG InstituteofMathematics AcademiaSinicaBeijing100080China InstitutfüdrMathematik UniversitaetWienA-1090Austria

The initial boundary value problems (IBVP) for the system of compressible adiabatic flow through porous media and the IBVP for its corresponding reduced system through Darcy’ laws on [0, 1] x [0, +] are considered respectively. The global existence of smooth solutions to the IBVP problems for two systems are proved, and their large-time behavior is analyzed. The time-asymptotic equivalence of these two systems are investigated, the decay rate of the difference of solutions between these two systems are shown to be determined explicitly by the initial perturbations and boundary effects. It is found that the oscillation of the specific volume can be cancelled by that of entropy, i.e., the oscillation of the specific volume and entropy is not required to be small.

关键词： Initial boundary value problem Global existence large-time behavior

THE ASYMPTOTIC STABILITY OF PHASE SEPARATION STATES FOR COMPRESSIBLE IMMISCIBLE TWO-PHASE FLOW IN 3D

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Acta Mathematica Scientia 2023年第5期43卷 2133-2158页

作者：陈亚洲 Hakho HONG 施小丁 College of Mathematics and Physics Beijing University of Chemical TechnologyBeijing 100029China Address Institute of Mathematics State Academy of SciencesPyongyangD P R Korea

This paper is concerned with a diffuse interface model called Navier-Stokes/CahnHilliard *** model is usually used to describe the motion of immiscible two-phase flows with a diffusion *** the periodic boundary value problem of this system in torus T3,we prove that there exists a global unique strong solution near the phase separation state,which means that no vacuum,shock wave,mass concentration,interface collision or rupture will be developed in finite ***,we establish the large time behavior of the global strong solution of this *** particular,we find that the phase field decays algebraically to the phase separation state.

关键词： Navier-Stokes/Cahn-Hilliard system strong solution existence uniqueness large-time behavior

REMARKS ON THE CAUCHY PROBLEM OF THE ONE-DIMENSIONAL VISCOUS RADIATIVE AND REACTIVE GAS

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Acta Mathematica Scientia 2020年第4期40卷 1020-1034页

作者： Yongkai LIAO Institute of Applied Physics and Computational Mathematics Beijing 100088China

This paper is concerned with the large-time behavior of solutions to the Cauchy problem of a one-dimensional viscous radiative and reactive *** on the elaborate energy estimates,we develop a new approach to derive the upper bound of the absolute temperature by avoiding the use of auxiliary functions Z(t)and W(t)introduced by Liao and Zhao[*** Equations,2018,265(5):2076-2120].Our results also improve upon the results obtained in Liao and Zhao[*** Equations,2018,265(5):2076-2120].

关键词： large-time behavior viscous radiative and reactive gas Cauchy problem large initial data

Convergence of the viscosity solution of non-autonomous Hamilton-Jacobi equations

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Science China Mathematics 2021年第8期64卷 1789-1800页

作者： Cui Chen Ya-Nan Wang Jun Yan The Faculty of Science Jiangsu UniversityZhenjiang 212013China School of Mathematical Sciences Nanjing Normal UniversityNanjing 210097China School of Mathematical Sciences Fudan UniversityShanghai 200433China Shanghai Key Laboratory for Contemporary Applied Mathematics Shanghai 200433China

In this paper,we investigate the non-autonomous Hamilton-Jacobi equation{ə_(t)u+H(t,x,ə_(x)=0,u(x,t)_(0))=φ(x),x∈M where H is 1-periodic with respect to t and M is a compact Riemannian manifold without *** obtain the viscosity solution denoted by T_(t_(0))^(t)φ(x)and show T_(t_(0))^(t)φ(x)converges uniformly to a time-periodic viscosity solution u^(*)(x,t)ofə_(t)u+H(t,x,ə_(x)u,u)=0.

关键词： Hamilton-Jacobi equation viscosity solution large-time behavior

Global classical solutions for 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip domain

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Science China Mathematics 2024年第11期67卷 2485-2514页

作者： Zefu Feng Guangyi Hong Changjiang Zhu School of Mathematical Sciences Chongqing Normal UniversityChongqing 401331China School of Mathematics South China University of TechnologyGuangzhou 510641China

In this paper,we consider 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip *** prominent character of the governing model is the presence of the microstructure,a linear coupling structure involving derivatives of the velocity fields,which along with the lack of spin viscosity brings several challenges to the *** exploiting the two-tier energy method developed in Guo and Tice(Arch Ration Mech Anal,2013),we prove the global existence of classical solutions to the governing model around a uniform magnetic field that is non-parallel to the horizontal ***,we show that the solution converges to the steady state at an almost exponential rate as time goes to *** of the main ingredients in our analysis,compared with previous works on micropolar fluids,is that we deal with the microstructure by establishing some delicate estimates based on the analysis of the div-curl decomposition,and the coupling between the fluid velocity and the vorticity of angular velocity.

关键词： magneto-micropolar fluids compressible global existence large-time behavior