On the low Mach number limit for the compressible Euler system

Abstract

In this paper, we propose a new approach to singular limits of inviscid fluid flows based on the concept of dissipative measure-valued solutions. We show that dissipative measure-valued solutions of the compressible Euler equations converge to the smooth solution of the incompressible Euler system when the Mach number tends to zero. This holds both for well-prepared and ill-prepared initial data, where in the latter case the presence of acoustic waves causes difficulties. However this effect is eliminated on unbounded domains thanks to dispersion.

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Cited by in corpus (8)

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• Low stratifucation of the complete Euler system
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• Low Mach and thin domain limit for the compressible Euler system
• Singular limits for compressible inviscid rotating fluids
• Dissipative Measure Valued Solutions to the Stochastic Compressible Navier-Stokes Equations and Inviscid-Incompressible Limit
• Mach limits in analytic spaces