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Dissipative solutions and semiflow selection for the complete Euler system
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SYSNO ASEP 0524628 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Dissipative solutions and semiflow selection for the complete Euler system Author(s) Breit, D. (GB)
Feireisl, Eduard (MU-W) RID, SAI, ORCID
Hofmanová, M. (DE)Source Title Communications in Mathematical Physics. - : Springer - ISSN 0010-3616
Roč. 376, č. 2 (2020), s. 1471-1497Number of pages 27 s. Language eng - English Country DE - Germany Keywords Euler system ; continuum fluid mechanics Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA18-05974S GA ČR - Czech Science Foundation (CSF) Method of publishing Open access Institutional support MU-W - RVO:67985840 UT WOS 000536053300016 EID SCOPUS 85078059145 DOI 10.1007/s00220-019-03662-7 Annotation To circumvent the ill-posedness issues present in various models of continuum fluid mechanics, we present a dynamical systems approach aiming at the selection of physically relevant solutions. Even under the presence of infinitely many solutions to the full Euler system describing the motion of a compressible inviscid fluid, our approach permits to select a system of solutions (one trajectory for every initial condition) satisfying the classical semiflow property. Moreover, the selection respects the well accepted admissibility criteria for physical solutions, namely, maximization of the entropy production rate and the weak–strong uniqueness principle. Consequently, strong solutions are always selected whenever they exist and stationary states are stable and included in the selection as well. To this end, we introduce a notion of dissipative solution, which is given by a triple of density, momentum and total entropy defined as expectations of a suitable measure-valued solution. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2021 Electronic address https://doi.org/10.1007/s00220-019-03662-7
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