Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591566 | Journal of Functional Analysis | 2009 | 47 Pages |
Abstract
This paper is devoted to solving globally the boundary value problem for the incompressible inhomogeneous Navier–Stokes equations in the half-space in the case of small data with critical regularity. In dimension n⩾3, we state that if the initial density ρ0 is close to a positive constant in and the initial velocity u0 is small with respect to the viscosity in the homogeneous Besov space then the equations have a unique global solution. The proof strongly relies on new maximal regularity estimates for the Stokes system in the half-space in , interesting for their own sake.
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