Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Volume 25, Issue 10, Pages 3831-3842Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdsb.2020079
Keywords
Euler system; weak solution; dissipative solution
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Funding
- Czech Sciences Foundation (GACR) [18-05974S]
- German Science Foundation DFG via the Collaborative Research Center [SFB1283]
- [RVO:67985840]
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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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