On the global existence and time decay estimates in critical spaces for the Navier–Stokes–Poisson system. Issue 13 (18th January 2017)

• Record Type: Journal Article
• Authors: Chikami, Noboru; Danchin, Raphaël
• Is Part Of: Mathematische Nachrichten. Volume 290:Issue 13(2017)
• Page Start: 1939
• Page End: 1970
• Publication Date: 2017-01-18
• Subjects: Compressible Navier–Stokes–Poisson system -- Besov spaces -- critical regularity -- decay estimates -- 35Qxx; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201600238
• Languages: English
• ISSNs: 0025-584X

Abstract

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 L 2 ‐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.