Asymptotic Behaviour of Solutions to the Navier-stokes Equations of a Two-dimensional Compressible Flow

作     者：Ying-hui ZHANG Zhong TAN 

作者机构：Department of Mathematics Hunan Institute of Science and Technology Yueyang 414006 China School of Mathematical Sciences Xiamen University Fujian 361005 China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2011年第27卷第4期

页      面：697-712页

核心收录：

学科分类：07[理学] 08[工学] 080103[工学-流体力学] 070104[理学-应用数学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Supported by the National Natural Science Foundation of China (No. 10976026) Hunan Provincial Natural Science Foundation of China (No. 10JJ6013) 

主　　题：asymptotic behaviour Navier-stokes equations compressible barotropic flow Orlicz spaces 

摘      要：In this paper, we are concerned with the asymptotic behaviour of a weak solution to the Navier-Stokes equations for compressible barotropic flow in two space dimensions with the pressure function satisfying p（g） = aglog^d（g） for large g. Here d 〉 2, a 〉 0. We introduce useful tools from the theory of Orlicz spaces and construct a suitable function which approximates the density for time going to infinity. Using properties of this function, we can prove the strong convergence of the density to its limit state. The behaviour of the velocity field and kinetic energy is also briefly discussed.