摘要
Abstract
In this article, the nonlinear stability of viscous shock wave for 1-D compressible Navier-Stokes system is studied. By the standard local existence method, it is found that the solution exists on a finite time interval [ 0,T] ( T < ￥) . However, this method is not available for global existence since the solution may blow up as time t tends to infinity. Thus a priori estimate needs to be established, which can reduce the upper bound of the solution on the time interval [ 0,T] . Moreover, the bound of the solution at time t = T is made equal to the bound at the initial time. By the same method, it is known the solution exists on [ T,2T] ,[ 2T, 3T] ,…. Thus the global existence of the solution is obtained. During the process of obtaining a priori estimate by the standard method, some additional conditions are proposed. To weaken those conditions, two suitable weighted functions were chosen, a double side weighted energy method was used, and a priori estimate was obtained under some weaker conditions. Thus when the adiabatic exponentγsatisfies 1 < γ <1.5, the solution not only exists globally but also tends to a viscous shock wave as time goes to infinity.关键词
initial value problem/viscous shock/asymptotic stabilityKey words
initial value problem/viscous shock/asymptotic stability分类
数理科学
