A-free rigidity and applications to the compressible Euler system

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00476952" target="_blank" >RIV/67985840:_____/17:00476952 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10231-016-0629-9" target="_blank" >http://dx.doi.org/10.1007/s10231-016-0629-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10231-016-0629-9" target="_blank" >10.1007/s10231-016-0629-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A-free rigidity and applications to the compressible Euler system

Popis výsledku v původním jazyce

Can every measure-valued solution to the compressible Euler equations be approximated by a sequence of weak solutions? We prove that the answer is negative: generalizing a well-known rigidity result of Ball and James to a more general situation, we construct an explicit measure-valued solution for the compressible Euler equations which cannot be generated by a sequence of distributional solutions. We also give an abstract necessary condition for measure-valued solutions to be generated by weak solutions, relying on work of Fonseca and Müller. While a priori it is not unexpected that not every measure-valued solution arises from a sequence of weak solutions, it is noteworthy that this observation in the compressible case is in contrast to the incompressible situation, where every measure-valued solution can be approximated by weak solutions, as shown by Székelyhidi and Wiedemann.

Název v anglickém jazyce

A-free rigidity and applications to the compressible Euler system

Popis výsledku anglicky

Can every measure-valued solution to the compressible Euler equations be approximated by a sequence of weak solutions? We prove that the answer is negative: generalizing a well-known rigidity result of Ball and James to a more general situation, we construct an explicit measure-valued solution for the compressible Euler equations which cannot be generated by a sequence of distributional solutions. We also give an abstract necessary condition for measure-valued solutions to be generated by weak solutions, relying on work of Fonseca and Müller. While a priori it is not unexpected that not every measure-valued solution arises from a sequence of weak solutions, it is noteworthy that this observation in the compressible case is in contrast to the incompressible situation, where every measure-valued solution can be approximated by weak solutions, as shown by Székelyhidi and Wiedemann.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA13-00522S" target="_blank" >GA13-00522S: Kvalitativní analýza a numerické řešení problémů proudění v obecně časově závislých oblastech s různými okrajovými podmínkami</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Annali di Matematica Pura ed Applicata

ISSN

0373-3114

e-ISSN

—

Svazek periodika

196

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

16

Strana od-do

1557-1572

Kód UT WoS článku

000406034400017

EID výsledku v databázi Scopus

2-s2.0-85008500241