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On convergence of approximate solutions to the compressible Euler system
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SYSNO ASEP 0532187 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On convergence of approximate solutions to the compressible Euler system Author(s) Feireisl, Eduard (MU-W) RID, SAI, ORCID
Hofmanová, M. (DE)Article number 11 Source Title Annals of PDE. - : Springer - ISSN 2524-5317
Roč. 6, č. 2 (2020)Number of pages 24 s. Language eng - English Country CH - Switzerland Keywords compressible Euler system ; convergence ; defect measure ; weak solution 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 000700356400005 EID SCOPUS 85090088581 DOI 10.1007/s40818-020-00086-8 Annotation We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence either (i) converges strongly in the energy norm, or (ii) the limit is not a weak solution of the associated Euler system. This is in sharp contrast to the incompressible case, where (oscillatory) approximate solutions may converge weakly to solutions of the Euler system. Our approach leans on identifying a system of differential equations satisfied by the associated turbulent defect measure and showing that it only has a trivial 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/s40818-020-00086-8
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