We prove a stability result of constant equilibria for the three dimensional Navier-Stokes-Poisson system uniform in the inviscid limit. We allow the initial density to be close to a constant and the potential part of the initial velocity to be small independently of the rescaled viscosity parameter ε while the incompressible part of the initial velocity is assumed to be small compared to ε. We then get a unique global smooth solution. We also prove a uniform in ε time decay rate for these solutions. Our approach allows to combine the parabolic energy estimates that are efficient for the viscous equation at ε fixed and the dispersive techniques (dispersive estimates and normal forms) that are useful for the inviscid irrotational system.
Cite this article
Frédéric Rousset, Changzhen Sun, Stability of equilibria uniformly in the inviscid limit for the Navier-Stokes-Poisson system. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 4, pp. 1255–1294DOI 10.1016/J.ANIHPC.2020.11.004