Inhomogeneous Navier-Stokes equations in the half-space, with only bounded density

Raphaël Danchin (1) , Ping Zhang (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 AMSS - Academy of Mathematics and Systems Science

In this paper, we establish the global existence of small solutions to the inhomo- geneous Navier-Stokes system in the half-space. The initial density only has to be bounded and close enough to a positive constant, and the initial velocity belongs to some critical Besov space. With a little bit more regularity for the initial velocity, those solutions are proved to be unique. In the last section of the paper, our results are partially extended to the bounded domain case.

Domaines: Equations aux dérivées partielles [math.AP]

Raphaël Danchin, Ping Zhang. Inhomogeneous Navier-Stokes equations in the half-space, with only bounded density. Journal of Functional Analysis, 2014, 267, pp.2371-2436. ⟨hal-00813552⟩