The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00542022" target="_blank" >RIV/67985840:_____/21:00542022 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1142/S0219891621500041" target="_blank" >https://doi.org/10.1142/S0219891621500041</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0219891621500041" target="_blank" >10.1142/S0219891621500041</a>
Alternative languages
Result language
angličtina
Original language name
The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings
Original language description
We consider the Cauchy problem for the barotropic Euler system coupled to Helmholtz or Poisson equations, in the whole space. We assume that the initial density is small enough, and that the initial velocity is close to some reference vector field u0 such that the spectrum of Du0 is positive and bounded away from zero. We prove the existence of a global unique solution with (fractional) Sobolev regularity, and algebraic time decay estimates. Our work extends Grassin and Serre’s papers [Existence de solutions globales et régulières aux équations d’Euler pour un gaz parfait isentropique, C. R. Acad. Sci. Paris Sér. I 325 (1997) 721–726, 1997, Global smooth solutions to Euler equations for a perfect gas, Indiana Univ. Math. J. 47 (1998) 1397–1432, Solutions classiques globales des équations d’Euler pour un fluide parfait compressible, Ann. Inst. Fourier Grenoble 47 (1997) 139–159] dedicated to the compressible Euler system without coupling and with integer regularity exponents.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA19-04243S" target="_blank" >GA19-04243S: Partial differential equations in mechanics and thermodynamics of fluids</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Hyperbolic Differential Equations
ISSN
0219-8916
e-ISSN
1793-6993
Volume of the periodical
18
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
25
Pages from-to
169-193
UT code for WoS article
000643737900004
EID of the result in the Scopus database
2-s2.0-85104939778