Dissipative solutions and semiflow selection for the complete Euler system

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00524628" target="_blank" >RIV/67985840:_____/20:00524628 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00220-019-03662-7" target="_blank" >https://doi.org/10.1007/s00220-019-03662-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00220-019-03662-7" target="_blank" >10.1007/s00220-019-03662-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Dissipative solutions and semiflow selection for the complete Euler system

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Dissipative solutions and semiflow selection for the complete Euler system

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-05974S" target="_blank" >GA18-05974S: Oscilace a koncentrace proti stabilitě v rovnicích pohybu tekutin</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Communications in Mathematical Physics

ISSN

0010-3616

e-ISSN

—

Svazek periodika

376

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

27

Strana od-do

1471-1497

Kód UT WoS článku

000536053300016

EID výsledku v databázi Scopus

2-s2.0-85078059145