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

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.

arXiv comment27pages. arXiv admin note: text overlap with arXiv:0911.4098 by other authors