ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

作     者：Hakho Hong Feimin Huang 

作者机构：Institute of Mathematics Academy of Sciences Pyonyang DPR of Korea Institute of Applied Mathematics Academy of Mathematics and System Science Chinese Academy of Sciences Beijing 100190 China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2012年第32卷第1期

页      面：389-412页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：partially supported by NSFC (10825102)for distinguished youth scholar supported by the CAS-TWAS postdoctoral fellowships (FR number:3240223274) AMSS in Chinese Academy of Sciences 

主　　题：compressible Navier-Stokes equations free boundary superposition of shockwave and contact discontinuity stability 

摘      要：A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is established under some smallness conditions. To do this, we first construct a new viscous contact wave such that the momentum equation is satisfied exactly and then determine the shift of the viscous shock wave. By using them together with an inequality concerning the heat kernel in the half space, we obtain the desired a priori estimates. The proof is based on the elementary energy method by the anti-derivative argument.