ON THE GLOBAL EXISTENCE OF SMOOTH SOLUTIONS TO THE MULTI-DIMENSIONAL COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDING DAMPING IN HALF SPACE

doi:10.1016/S0252-9602(17)30050-4

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (4): 949-964.doi: 10.1016/S0252-9602(17)30050-4

ON THE GLOBAL EXISTENCE OF SMOOTH SOLUTIONS TO THE MULTI-DIMENSIONAL COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDING DAMPING IN HALF SPACE

侯飞

Department of Mathematics and IMS, Nanjing University, Nanjing 210093, China

收稿日期:2016-06-28 修回日期:2016-12-26 出版日期:2017-08-25 发布日期:2017-08-25
作者简介:Fei HOU,E-mail:houfeimath@gmail.com

ON THE GLOBAL EXISTENCE OF SMOOTH SOLUTIONS TO THE MULTI-DIMENSIONAL COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDING DAMPING IN HALF SPACE

Fei HOU

Department of Mathematics and IMS, Nanjing University, Nanjing 210093, China

Received:2016-06-28 Revised:2016-12-26 Online:2017-08-25 Published:2017-08-25
About author:Fei HOU,E-mail:houfeimath@gmail.com

摘要/Abstract

摘要：

This paper is a continue work of[4, 5]. In the previous two papers, we studied the Cauchy problem of the multi-dimensional compressible Euler equations with time-depending damping term -(μ/(1+t)^λ)ρu, where λ ≥ 0 and μ > 0 are constants. We have showed that, for all λ ≥ 0 and μ > 0, the smooth solution to the Cauchy problem exists globally or blows up in finite time. In the present paper, instead of the Cauchy problem we consider the initialboundary value problem in the half space R₊^d with space dimension d=2, 3. With the help of the special structure of the equations and the fluid vorticity, we overcome the difficulty arisen from the boundary effect. We prove that there exists a global smooth solution for 0 ≤ λ < 1 when the initial data is close to its equilibrium state. In addition, exponential decay of the fluid vorticity will also be established.

关键词: compressible Euler equations, initial-boundary value problem, damping, global existence

Abstract:

Key words: compressible Euler equations, initial-boundary value problem, damping, global existence

侯飞. ON THE GLOBAL EXISTENCE OF SMOOTH SOLUTIONS TO THE MULTI-DIMENSIONAL COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDING DAMPING IN HALF SPACE[J]. 数学物理学报(英文版), 2017, 37(4): 949-964.

Fei HOU. ON THE GLOBAL EXISTENCE OF SMOOTH SOLUTIONS TO THE MULTI-DIMENSIONAL COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDING DAMPING IN HALF SPACE[J]. Acta mathematica scientia,Series B, 2017, 37(4): 949-964.

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ON THE GLOBAL EXISTENCE OF SMOOTH SOLUTIONS TO THE MULTI-DIMENSIONAL COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDING DAMPING IN HALF SPACE

ON THE GLOBAL EXISTENCE OF SMOOTH SOLUTIONS TO THE MULTI-DIMENSIONAL COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDING DAMPING IN HALF SPACE

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