A-free rigidity and applications to the compressible Euler system
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
A-free rigidity and applications to the compressible Euler system
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA13-00522S" target="_blank" >GA13-00522S: Qualitative analysis and numerical solution of problems of flows in generally time-dependent domains with various boundary conditions</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annali di Matematica Pura ed Applicata
ISSN
0373-3114
e-ISSN
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Volume of the periodical
196
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
16
Pages from-to
1557-1572
UT code for WoS article
000406034400017
EID of the result in the Scopus database
2-s2.0-85008500241