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Formation of singularities and existence of global continuous solutions for the compressible euler equations

Abstract:

We are concerned with the formation of singularities and the existence of global continuous solutions of the Cauchy problem for the one-dimensional nonisentropic Euler equations for compressible fluids. For the isentropic Euler equations, we pinpoint a necessary and sufficient condition for the formation of singularities of solutions with large initial data that allow a far-field vacuum---there exists a compression in the initial data. For the nonisentropic Euler equations, we identify a suff...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1137/20M1316603

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Keble College
Role:
Author
ORCID:
0000-0001-5146-3839
Publisher:
Society for Industrial and Applied Mathematics Publisher's website
Journal:
SIAM Journal on Mathematical Analysis Journal website
Volume:
53
Issue:
6
Pages:
6280-6325
Publication date:
2021-11-04
Acceptance date:
2021-07-09
DOI:
EISSN:
1095-7154
ISSN:
0036-1410
Language:
English
Keywords:
Pubs id:
1232933
Local pid:
pubs:1232933
Deposit date:
2022-02-04

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