Nonuniqueness of admissible weak solution to the Riemann problem for the full Euler system in two dimensions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00524230" target="_blank" >RIV/67985840:_____/20:00524230 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1137/18M1190872" target="_blank" >https://doi.org/10.1137/18M1190872</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/18M1190872" target="_blank" >10.1137/18M1190872</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Nonuniqueness of admissible weak solution to the Riemann problem for the full Euler system in two dimensions

Popis výsledku v původním jazyce

The question of well- and ill-posedness of entropy admissible solutions to the multi-dimensional systems of conservation laws has been studied recently in the case of isentropic Euler equations. In this context special initial data were considered, namely the 1D Riemann problem which is extended trivially to a second space dimension. It was shown that there exist infinitely many bounded entropy admissible weak solutions to such a 2D Riemann problem for isentropic Euler equations if the initial data give rise to a 1D self-similar solution containing a shock. In this work we study such a 2D Riemann problem for the full Euler system in two space dimensions and prove the existence of infinitely many bounded entropy admissible weak solutions in the case that the Riemann initial data give rise to the 1D self-similar solution consisting of two shocks and possibly a contact discontinuity.

Název v anglickém jazyce

Nonuniqueness of admissible weak solution to the Riemann problem for the full Euler system in two dimensions

Popis výsledku anglicky

The question of well- and ill-posedness of entropy admissible solutions to the multi-dimensional systems of conservation laws has been studied recently in the case of isentropic Euler equations. In this context special initial data were considered, namely the 1D Riemann problem which is extended trivially to a second space dimension. It was shown that there exist infinitely many bounded entropy admissible weak solutions to such a 2D Riemann problem for isentropic Euler equations if the initial data give rise to a 1D self-similar solution containing a shock. In this work we study such a 2D Riemann problem for the full Euler system in two space dimensions and prove the existence of infinitely many bounded entropy admissible weak solutions in the case that the Riemann initial data give rise to the 1D self-similar solution consisting of two shocks and possibly a contact discontinuity.

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

2020

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Mathematical Analysis

ISSN

0036-1410

e-ISSN

—

Svazek periodika

52

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

1729-1760

Kód UT WoS článku

000546971100024

EID výsledku v databázi Scopus

2-s2.0-85084422987