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

被引：20

作者：

Chikami, Noboru ^{[1
]}

Danchin, Raphael ^{[2
,3
]}

机构：

[1] Tohoku Univ, Math Inst, Sendai, Miyagi 9808578, Japan

[2] Univ Paris Est, UMR 8050, LAMA, 61 Ave Gen Gaulle, F-94010 Creteil, France

[3] Inst Univ France, 61 Ave Gen Gaulle, F-94010 Creteil, France

来源：

MATHEMATISCHE NACHRICHTEN | 2017年 / 290卷 / 13期

关键词：

Compressible Navier-Stokes-Poisson system; Besov spaces; critical regularity; decay estimates; WELL-POSEDNESS; EQUATIONS;

D O I：

10.1002/mana.201600238

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：1939 / 1970

页数：32

共 27 条

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