The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings

0542022 - MÚ 2022 RIV US eng J - Journal Article
Blanc, X. - Danchin, R. - Ducomet, B. - Nečasová, Šárka
The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings.
Journal of Hyperbolic Differential Equations. Roč. 18, č. 1 (2021), s. 169-193. ISSN 0219-8916. E-ISSN 1793-6993
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : compressible Euler system * Helmholtz-Poisson * global solution
OECD category: Pure mathematics
Impact factor: 0.635, year: 2021
Method of publishing: Limited access
https://doi.org/10.1142/S0219891621500041

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.
Permanent Link: http://hdl.handle.net/11104/0319518