Ill-posedness of the Kelvin-Helmholtz problem for compressible Euler fluids

Binqiang Xie; Bin Zhao

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arXiv · 2407.01938

Ill-posedness of the Kelvin-Helmholtz problem for compressible Euler fluids

Binqiang Xie·Bin Zhao

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Abstract

In this paper, when the magnitude of the Mach number is strictly between some fixed small enough constant and $\sqrt{2}$, we can prove the linear and nonlinear ill-posedness of the Kelvin-Helmholtz problem for compressible ideal fluids. To our best knowledge, this is the first reslult that proves the nonlinear ill-posedness to the Kelvin-Helmholtz problem for the compressible Euler fluids.

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Binqiang Xie, Bin Zhao. 2024-07-02. Ill-posedness of the Kelvin-Helmholtz problem for compressible Euler fluids. https://arxiv.org/abs/2407.01938

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