GLOBAL INSTABILITY OF MULTI-DIMENSIONAL PLANE SHOCKS FOR ISOTHERMAL FLOW  

作　　者：Ning-An LAI Wei XIANG Yi ZHOU 赖宁安;向伟;周忆(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China Department of Mathematics,Lishui University,Lishui 323000,China;Department of Mathematics,City University of Hong Kong,Kowloon,Hong Kong 999077,China;School of Mathematical Sciences,Fudan University,Shanghai 200433,China)

机构地区：[1]College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China Department of Mathematics,Lishui University,Lishui 323000,China [2]Department of Mathematics,City University of Hong Kong,Kowloon,Hong Kong 999077,China [3]School of Mathematical Sciences,Fudan University,Shanghai 200433,China

出　　处：《Acta Mathematica Scientia》2022年第3期887-902,共16页数学物理学报（B辑英文版）

基　　金：supported by NSFC(12171097);supported in part by the Research Grants Council of the HKSAR,China(Project No.CityU 11303518,Project CityU 11304820 and Project CityU 11300021).

摘　　要：In this paper,we are concerned with the long time behavior of the piecewise smooth solutions to the generalized Riemann problem governed by the compressible isothermal Euler equations in two and three dimensions.A non-existence result is established for the fan-shaped wave structure solution,including two shocks and one contact discontinuity which is a perturbation of plane waves.Therefore,unlike in the one-dimensional case,the multi-dimensional plane shocks are not stable globally.Moreover,a sharp lifespan estimate is established which is the same as the lifespan estimate for the nonlinear wave equations in both two and three space dimensions.

关 键 词：BLOW-UP global solution instability shock contact disctinuity Euler equations ISOTHERMAL generalized Riemann problem nonlinear wave equations 

分 类 号：O186.12[理学—数学]