Solution Semiflow to the isentropic Euler system

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00522128" target="_blank" >RIV/67985840:_____/20:00522128 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00205-019-01420-6" target="_blank" >https://doi.org/10.1007/s00205-019-01420-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00205-019-01420-6" target="_blank" >10.1007/s00205-019-01420-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Solution Semiflow to the isentropic Euler system

Popis výsledku v původním jazyce

It is nowadays well understood that the multidimensional isentropic Euler system is desperately ill-posed. Even certain smooth initial data give rise to infinitely many solutions and all available selection criteria fail to ensure both global existence and uniqueness. We propose a different approach to the well-posedness of this system based on ideas from the theory of Markov semigroups: we show the existence of a Borel measurable solution semiflow. To this end, we introduce a notion of dissipative solution which is understood as time dependent trajectories of the basic state variables—the mass density, the linear momentum, and the energy—in a suitable phase space. The underlying system of PDEs is satisfied in a generalized sense. The solution semiflow enjoys the standard semigroup property and the solutions coincide with the strong solutions as long as the latter exist. Moreover, they minimize the energy (maximize the energy dissipation) among all dissipative solutions.

Název v anglickém jazyce

Solution Semiflow to the isentropic Euler system

Popis výsledku anglicky

It is nowadays well understood that the multidimensional isentropic Euler system is desperately ill-posed. Even certain smooth initial data give rise to infinitely many solutions and all available selection criteria fail to ensure both global existence and uniqueness. We propose a different approach to the well-posedness of this system based on ideas from the theory of Markov semigroups: we show the existence of a Borel measurable solution semiflow. To this end, we introduce a notion of dissipative solution which is understood as time dependent trajectories of the basic state variables—the mass density, the linear momentum, and the energy—in a suitable phase space. The underlying system of PDEs is satisfied in a generalized sense. The solution semiflow enjoys the standard semigroup property and the solutions coincide with the strong solutions as long as the latter exist. Moreover, they minimize the energy (maximize the energy dissipation) among all dissipative solutions.

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

Archive for Rational Mechanics and Analysis

ISSN

0003-9527

e-ISSN

—

Svazek periodika

235

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

28

Strana od-do

167-194

Kód UT WoS článku

000522430900006

EID výsledku v databázi Scopus

2-s2.0-85069473027