Dissipative solutions and semiflow selection for the complete Euler system

0524628 - MÚ 2021 RIV DE eng J - Journal Article
Breit, D. - Feireisl, Eduard - Hofmanová, M.
Dissipative solutions and semiflow selection for the complete Euler system.
Communications in Mathematical Physics. Roč. 376, č. 2 (2020), s. 1471-1497. ISSN 0010-3616. E-ISSN 1432-0916
R&D Projects: GA ČR(CZ) GA18-05974S
Institutional support: RVO:67985840
Keywords : Euler system * continuum fluid mechanics
OECD category: Pure mathematics
Impact factor: 2.386, year: 2020
Method of publishing: Open access
https://doi.org/10.1007/s00220-019-03662-7

To circumvent the ill-posedness issues present in various models of continuum fluid mechanics, we present a dynamical systems approach aiming at the selection of physically relevant solutions. Even under the presence of infinitely many solutions to the full Euler system describing the motion of a compressible inviscid fluid, our approach permits to select a system of solutions (one trajectory for every initial condition) satisfying the classical semiflow property. Moreover, the selection respects the well accepted admissibility criteria for physical solutions, namely, maximization of the entropy production rate and the weak–strong uniqueness principle. Consequently, strong solutions are always selected whenever they exist and stationary states are stable and included in the selection as well. To this end, we introduce a notion of dissipative solution, which is given by a triple of density, momentum and total entropy defined as expectations of a suitable measure-valued solution.
Permanent Link: http://hdl.handle.net/11104/0308965