On global well/ill-posedness of the Euler-Poisson system

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00458906" target="_blank" >RIV/67985840:_____/16:00458906 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-0348-0939-9_12" target="_blank" >http://dx.doi.org/10.1007/978-3-0348-0939-9_12</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-0348-0939-9_12" target="_blank" >10.1007/978-3-0348-0939-9_12</a>

Result language
angličtina
Original language name
On global well/ill-posedness of the Euler-Poisson system
Original language description
We discuss the problem of well-posedness of the Euler-Poisson system arising, for example, in the theory of semi-conductors, models of plasma and gaseous stars in astrophysics. We introduce the concept of dissipative weak solution satisfying, in addition to the standard system of integral identities replacing the original system of partial differential equations, the balance of total energy, together with the associated relative entropy inequality. We show that strong solutions are unique in the class of dissipative solutions (weak-strong uniqueness). Finally, we use the method of convex integration to show that the Euler-Poisson system may admit even infinitely many weak dissipative solutions emanating from the same initial data.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Recent Developments of Mathematical Fluid Mechanics
ISBN
978-3-0348-0938-2
ISSN
2297-0320
e-ISSN
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Number of pages
17
Pages from-to
215-231
Publisher name
Springer
Place of publication
Basel
Event location
Nara
Event date
Mar 5, 2013
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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