Uniform stability in the inviscid limit of equilibria for the Navier-Stokes-Poisson system

In this presentation, I will talk about a joint work with Frédéric Rousset on the uniform (in the rescaled small viscosity parameter) stability of the 3d Navier-Stokes-Poisson (NSP) system.
In this work, we establish a global well-posedness result for NSP by allowing 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 should be small compared to ε.
To obtain this result, we propose a method that can combine the techniques from dispersive PDEs (more precisely, normal form transformation) and the classical parabolic
energy estimates used in fluid mechanics.
At the end of the presentation, I will present some applications of the method used in this work and also the related work for 2d NSP.