带阻尼的二维等熵可压缩欧拉方程组不稳定激波的生成

Abstract

Abstract:

In this paper, we consider the unstable blowup mechanism for 2D isentropic compressible Euler equations with damping under azimuthal symmetry. We construct a suitable self-similar coordinate transformation for the damped Euler equations which is different from the general Euler equations. Besides, we also choose a kind of initial data which asymptotically converges to the unstable $C^{{1}/{5}}$ self-similar solution of the Burgers equation with damping. In addition, we introduce the modulation variables and the Newton iteration to describe the unstable shock. Further, the blowup profile has a cusp singularity of $C^{{1}/{5}}$ Hölder regularity at the blowup time.

Key words: compressible Euler equations, damping, unstable shock, modulation variables.

CLC Number:

O175.2

Wanqing Zhu. The Unstable Shock Formation for 2D Isentropic Compressible Euler Equations with Damping[J].Acta mathematica scientia,Series A, 2026, 46(6): 2140-2166.

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References 17

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The Unstable Shock Formation for 2D Isentropic Compressible Euler Equations with Damping

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