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The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings
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SYSNO ASEP 0542022 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings Author(s) Blanc, X. (FR)
Danchin, R. (FR)
Ducomet, B. (FR)
Nečasová, Šárka (MU-W) RID, SAI, ORCIDSource Title Journal of Hyperbolic Differential Equations . - : World Scientific Publishing - ISSN 0219-8916
Roč. 18, č. 1 (2021), s. 169-193Number of pages 25 s. Language eng - English Country US - United States Keywords compressible Euler system ; Helmholtz-Poisson ; global solution Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA19-04243S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000643737900004 EID SCOPUS 85104939778 DOI 10.1142/S0219891621500041 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2022 Electronic address https://doi.org/10.1142/S0219891621500041
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