初值间断的可压缩Navier-Stokes方程弱解的存在性  

Existence of Weak Solution to Compressible Navier-Stokes Equation with Discontinuous Initial Data

作　　者：王军礼[1] 龚六堂[2] 连汝续[3] WANG JUNLI GONG LIUTANG LIAN Ruxu(School of Mathematical Sciences, Capital Normal University, Beijing 100048, China Guanghua School of Management, Peking University, Beijing 100871, China College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China)

机构地区：[1]首都师范大学数学科学学院,北京100048 [2]北京大学光华管理学院,北京100871 [3]华北水利水电大学数学与信息科学学院,郑州200241

出　　处：《应用数学学报》2017年第1期121-135,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11101145;11301431)资助项目

摘　　要：本文研究了粘性系数依赖密度的一维可压缩Navier-Stokes方程的初值间断问题.当初始密度间断任意大时,证明了一维可压缩Navier-Stokes方程固定边界问题整体弱解的存在唯一性,分段正则性,并给出了弱解的大时间行为等.This paper is concerned with the initial boundary value problem for one-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosity coefficients and discontinuous initial data. We prove that there exists a unique global weak solution for piecewise regular initial density with arbitrarily large jump discontinuity. Moreover, we show that the jump of density decays exponentially in time and the piecewise regular solution tends to the equilibrium state exponentially as time tends to infinity.

关 键 词：Navier—Stokes方程 初值间断 弱解 存在唯—性 大时间行为 

分 类 号：O175.2[理学—数学]