On global well/ill-posedness of the Euler-Poisson system

0458906 - MÚ 2017 RIV CH eng C - Conference Paper (international conference)
Feireisl, Eduard
On global well/ill-posedness of the Euler-Poisson system.
Recent Developments of Mathematical Fluid Mechanics. Basel: Springer, 2016 - (Amann, H.; Giga, Y.; Kozono, H.; Okamoto, H.; Yamazaki, M.), s. 215-231. Advances in Mathematical Fluid Mechanics. ISBN 978-3-0348-0938-2. ISSN 2297-0320.
[International Conference on Mathematical Fluid Dynamics on the Occasion of Yoshihiro Shibata’s 60th Birthday. Nara (JP), 05.03.2013-09.03.2013]
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : dissipative solution * Euler-Poisson system * weak solution
Subject RIV: BA - General Mathematics
http://link.springer.com/chapter/10.1007%2F978-3-0348-0939-9_12

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.
Permanent Link: http://hdl.handle.net/11104/0259119