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 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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