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arXiv · 1710.10918

On oscillatory solutions to the complete Euler system

Eduard Feireisl·Christian Klingenberg·Ondřej Kreml·Simon Markfelder
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Abstract

The Euler system in fluid dynamics is a model of a compressible inviscid fluid incorporating the three basic physical principles: Conservation of mass, momentum, and energy. We show that the Cauchy problem is basically ill-posed for the $L^\infty$-initial data in the class of weak entropy solutions. As a consequence, there are infinitely many measure-valued solutions for a vast set of initial data. Finally, using the concept of relative energy, we discuss a singular limit problem for the measure-valued solutions, where the Mach and Froude number are proportional to a small parameter.

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Eduard Feireisl, Christian Klingenberg, Ondřej Kreml, Simon Markfelder. 2017-10-30. On oscillatory solutions to the complete Euler system. https://doi.org/10.1016/j.jde.2020.01.018

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