Dissipative Solutions and Semiflow Selection for the Complete Euler System

Breit D, Feireisl E, Hofmanová M (2020)
COMMUNICATIONS IN MATHEMATICAL PHYSICS 376(2): 1471-1497.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Breit, Dominic; Feireisl, Eduard; Hofmanová, MartinaUniBi
Abstract / Bemerkung
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.
Erscheinungsjahr
2020
Zeitschriftentitel
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Band
376
Ausgabe
2
Seite(n)
1471-1497
ISSN
0010-3616
eISSN
1432-0916
Page URI
https://pub.uni-bielefeld.de/record/2944193

Zitieren

Breit D, Feireisl E, Hofmanová M. Dissipative Solutions and Semiflow Selection for the Complete Euler System. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2020;376(2):1471-1497.
Breit, D., Feireisl, E., & Hofmanová, M. (2020). Dissipative Solutions and Semiflow Selection for the Complete Euler System. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 376(2), 1471-1497. doi:10.1007/s00220-019-03662-7
Breit, D., Feireisl, E., and Hofmanová, M. (2020). Dissipative Solutions and Semiflow Selection for the Complete Euler System. COMMUNICATIONS IN MATHEMATICAL PHYSICS 376, 1471-1497.
Breit, D., Feireisl, E., & Hofmanová, M., 2020. Dissipative Solutions and Semiflow Selection for the Complete Euler System. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 376(2), p 1471-1497.
D. Breit, E. Feireisl, and M. Hofmanová, “Dissipative Solutions and Semiflow Selection for the Complete Euler System”, COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 376, 2020, pp. 1471-1497.
Breit, D., Feireisl, E., Hofmanová, M.: Dissipative Solutions and Semiflow Selection for the Complete Euler System. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 376, 1471-1497 (2020).
Breit, Dominic, Feireisl, Eduard, and Hofmanová, Martina. “Dissipative Solutions and Semiflow Selection for the Complete Euler System”. COMMUNICATIONS IN MATHEMATICAL PHYSICS 376.2 (2020): 1471-1497.

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