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On global well/ill-posedness of the Euler-Poisson system
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SYSNO ASEP 0458906 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title On global well/ill-posedness of the Euler-Poisson system Author(s) Feireisl, Eduard (MU-W) RID, SAI, ORCID Source Title Recent Developments of Mathematical Fluid Mechanics. - Basel : Springer, 2016 / Amann H. ; Giga Y. ; Kozono H. ; Okamoto H. ; Yamazaki M. - ISSN 2297-0320 - ISBN 978-3-0348-0938-2 Pages s. 215-231 Number of pages 17 s. Publication form Print - P Action International Conference on Mathematical Fluid Dynamics on the Occasion of Yoshihiro Shibata’s 60th Birthday Event date 05.03.2013 - 09.03.2013 VEvent location Nara Country JP - Japan Event type WRD Language eng - English Country CH - Switzerland Keywords dissipative solution ; Euler-Poisson system ; weak solution Subject RIV BA - General Mathematics Institutional support MU-W - RVO:67985840 EID SCOPUS 84964199901 DOI 10.1007/978-3-0348-0939-9_12 Annotation We discuss the problem of well-posedness of the Euler-Poisson system arising, for example, in the theory of semi-conductors, models of plasma and gaseous stars in astrophysics. We introduce the concept of dissipative weak solution satisfying, in addition to the standard system of integral identities replacing the original system of partial differential equations, the balance of total energy, together with the associated relative entropy inequality. We show that strong solutions are unique in the class of dissipative solutions (weak-strong uniqueness). Finally, we use the method of convex integration to show that the Euler-Poisson system may admit even infinitely many weak dissipative solutions emanating from the same initial data. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2017
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