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arXiv · 1911.08978

Stability of equilibria uniformly in the inviscid limit for the Navier-Stokes-Poisson system

Frédéric Rousset·Changzhen Sun
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Abstract

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 $\varepsilon$ while the incompressible part of the initial velocity is assumed to be small compared to $\varepsilon$. We then get a unique global smooth solution. We also prove a uniform in $\varepsilon$ time decay rate for these solutions. Our approach allows to combine the parabolic energy estimates that are efficient for the viscous equation at $\varepsilon$ fixed and the dispersive techniques (dispersive estimates and normal form transformation) that are useful for the inviscid irrotational system.

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Frédéric Rousset, Changzhen Sun. 2019-11-20. Stability of equilibria uniformly in the inviscid limit for the Navier-Stokes-Poisson system. https://arxiv.org/abs/1911.08978

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