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Generalized solutions to models of inviscid fluids

M.H. gratefully acknowledges the financial support by the German Science Foundation DFG via the Collaborative Research Center SFB1283

The research of E.F. leading to these results has received funding from the Czech Sciences Foundation (GAČR), Grant Agreement 18–05974S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by 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.

    Mathematics Subject Classification: 35D30, 35A01, 35Q31.


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