On strong continuity of weak solutions to the compressible Euler system

0541263 - MÚ 2022 RIV US eng J - Journal Article
Abbatiello, A. - Feireisl, Eduard
On strong continuity of weak solutions to the compressible Euler system.
Journal of Nonlinear Science. Roč. 31, č. 2 (2021), č. článku 33. ISSN 0938-8974. E-ISSN 1432-1467
R&D Projects: GA ČR(CZ) GA18-05974S
Institutional support: RVO:67985840
Keywords : compressible Euler system * convex integration * oscillatory lemma * weak solution
OECD category: Pure mathematics
Impact factor: 3.443, year: 2021
Method of publishing: Limited access
https://doi.org/10.1007/s00332-021-09694-5

Let S={τn}n=1∞⊂(0,T) be an arbitrary countable (dense) set. We show that for any given initial density and momentum, the compressible Euler system admits (infinitely many) admissible weak solutions that are not strongly continuous at each τn, n= 1 , 2 , ⋯. The proof is based on a refined version of the oscillatory lemma of De Lellis and Székelyhidi with coefficients that may be discontinuous on a set of zero Lebesgue measure.
Permanent Link: http://hdl.handle.net/11104/0318853