On uniqueness of dissipative solutions to the isentropic Euler system

0508339 - MÚ 2020 RIV US eng J - Journal Article
Feireisl, Eduard - Ghoshal, S.S. - Jana, A.
On uniqueness of dissipative solutions to the isentropic Euler system.
Communications in Partial Differential Equations. Roč. 44, č. 12 (2019), s. 1285-1298. ISSN 0360-5302. E-ISSN 1532-4133
R&D Projects: GA ČR(CZ) GA18-05974S
Institutional support: RVO:67985840
Keywords : compressible fluid * dissipative solution * Euler system * weak solution
OECD category: Pure mathematics
Impact factor: 1.079, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1080/03605302.2019.1629958

The dissipative solutions can be seen as a convenient generalization of the concept of weak solution to the isentropic Euler system. They can be seen as expectations of the Young measures associated to a suitable measure-valued solution of the problem. We show that dissipative solutions coincide with weak solutions starting from the same initial data on condition that: (i) the weak solution enjoys certain Besov regularity, (ii) the symmetric velocity gradient of the weak solution satisfies a one-sided Lipschitz bound.
Permanent Link: http://hdl.handle.net/11104/0299270