Generalized solutions to models of inviscid fluids

Dominic Breit; Eduard Feireisl; Martina Hofmanová

doi:10.3934/dcdsb.2020079

Generalized solutions to models of inviscid fluids

Dominic Breit, Eduard Feireisl, Martina Hofmanová

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Abstract

We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible oscillations and/or concentrations in the associated generating sequence. Unlike the conventional measure–valued solutions or rather their expected values, the dissipative solutions comply with a natural compatibility condition – they are classical solutions as long as they enjoy a certain degree of smoothness.

Original language	English
Pages (from-to)	3831-3842
Number of pages	12
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	25
Issue number	10
Early online date	19 Jan 2020
DOIs	https://doi.org/10.3934/dcdsb.2020079
Publication status	Published - Oct 2020

Keywords

Dissipative solution
Euler system
Weak solution

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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abstract = "We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible oscillations and/or concentrations in the associated generating sequence. Unlike the conventional measure–valued solutions or rather their expected values, the dissipative solutions comply with a natural compatibility condition – they are classical solutions as long as they enjoy a certain degree of smoothness.",

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AU - Feireisl, Eduard

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AB - We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible oscillations and/or concentrations in the associated generating sequence. Unlike the conventional measure–valued solutions or rather their expected values, the dissipative solutions comply with a natural compatibility condition – they are classical solutions as long as they enjoy a certain degree of smoothness.

KW - Dissipative solution

KW - Euler system

KW - Weak solution

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ER -

Generalized solutions to models of inviscid fluids

Abstract

Keywords

ASJC Scopus subject areas

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