Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00541167" target="_blank" >RIV/67985840:_____/21:00541167 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/21:10441305

Výsledek na webu

<a href="https://doi.org/10.1090/tran/8129" target="_blank" >https://doi.org/10.1090/tran/8129</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/tran/8129" target="_blank" >10.1090/tran/8129</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data

Popis výsledku v původním jazyce

We consider the isentropic Euler equations of gas dynamics in the whole two-dimensional space and we prove the existence of a C∞ initial datum which admits infinitely many bounded admissible weak solutions. Taking advantage of the relation between smooth solutions to the Euler system and to the Burgers equation we construct a smooth compression wave which collapses into a perturbed Riemann state at some time instant T > 0. In order to continue the solution after the formation of the discontinuity, we adjust and apply the theory developed by De Lellis and Székelyhidi [Ann. of Math. (2) 170 (2009), no. 3, pp. 1417–1436, Arch. Ration. Mech. Anal. 195 (2010), no. 1, pp. 225–260] and we construct infinitely many solutions. We introduce the notion of an admissible generalized fan subsolution to be able to handle data which are not piecewise constant and we reduce the argument to finding a single generalized subsolution.

Název v anglickém jazyce

Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data

Popis výsledku anglicky

We consider the isentropic Euler equations of gas dynamics in the whole two-dimensional space and we prove the existence of a C∞ initial datum which admits infinitely many bounded admissible weak solutions. Taking advantage of the relation between smooth solutions to the Euler system and to the Burgers equation we construct a smooth compression wave which collapses into a perturbed Riemann state at some time instant T > 0. In order to continue the solution after the formation of the discontinuity, we adjust and apply the theory developed by De Lellis and Székelyhidi [Ann. of Math. (2) 170 (2009), no. 3, pp. 1417–1436, Arch. Ration. Mech. Anal. 195 (2010), no. 1, pp. 225–260] and we construct infinitely many solutions. We introduce the notion of an admissible generalized fan subsolution to be able to handle data which are not piecewise constant and we reduce the argument to finding a single generalized subsolution.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ17-01694Y" target="_blank" >GJ17-01694Y: Matematická analýza parciálních diferenciálních rovnic popisujících nevazké proudění</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

American Mathematical Society. Transactions

ISSN

0002-9947

e-ISSN

1088-6850

Svazek periodika

374

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

2269-2295

Kód UT WoS článku

000625870700001

EID výsledku v databázi Scopus

2-s2.0-85094614183