Dissipative solutions and semiflow selection for the complete Euler system

Dominic Breit, Eduard Feireisl, Martina Hofmanová

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)
38 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)1471-1497
Number of pages27
JournalCommunications in Mathematical Physics
Issue number2
Early online date13 Jan 2020
Publication statusPublished - Jun 2020

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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