GLOBAL INSTABILITY OF MULTI-DIMENSIONAL PLANE SHOCKS FOR ISOTHERMAL FLOW

doi:10.1007/s10473-022-0305-7

Abstract

Abstract: 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.

Key words: Blow-up, global solution, instability, shock, contact disctinuity, Euler equations, isothermal, generalized Riemann problem, nonlinear wave equations

CLC Number:

35L60

Ning-An LAI, Wei XIANG, Yi ZHOU. GLOBAL INSTABILITY OF MULTI-DIMENSIONAL PLANE SHOCKS FOR ISOTHERMAL FLOW[J].Acta mathematica scientia,Series B, 2022, 42(3): 887-902.

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