On the global existence and time decay estimates in critical spaces for the Navier–Stokes–Poisson system

Noboru Chikami, Raphaël Danchin

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We are concerned with the study of the Cauchy problem for the Navier–Stokes–Poisson system in the critical regularity framework. In the case of a repulsive potential, we first establish the unique global solvability in any dimension n≥2 for small perturbations of a linearly stable constant state. Next, under a suitable additional condition involving only the low frequencies of the data and in the L2-critical framework (for simplicity), we exhibit optimal decay estimates for the constructed global solutions, which are similar to those of the barotropic compressible Navier–Stokes system. Our results rely on new a priori estimates for the linearized Navier–Stokes–Poisson system about a stable constant equilibrium, and on a refined time-weighted energy functional.

Original languageEnglish
Pages (from-to)1939-1970
Number of pages32
JournalMathematische Nachrichten
Volume290
Issue number13
DOIs
Publication statusPublished - 2017 Sep

Keywords

  • 35Qxx
  • Besov spaces
  • Compressible Navier–Stokes–Poisson system
  • critical regularity
  • decay estimates

ASJC Scopus subject areas

  • Mathematics(all)

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