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A critical functional framework for the inhomogeneous Navier-Stokes equations in the half-space

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 rho(0) is close to a positive constant in L(infinity) boolean AND (W) over dot(n)(1) (R(+)(n)) and the initial velocity u(0) is small with respect to the viscosity in the homogeneous Besov space (B) over dot(n,1)(0) (R(+)(n)) then the equations have a unique global solution. The proofstrongly relies on new maximal regularity estimates for the Stokes system in the half-space in L(1) (0, T: (B)over dot(p,1)(0)(R(+)(n))), interesting tor their own sake. (C) 2008 Elsevier Inc. All rights reserved.
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Submitted on : Tuesday, May 1, 2012 - 7:48:13 PM
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Raphaël Danchin, Piotr Boguslaw Mucha. A critical functional framework for the inhomogeneous Navier-Stokes equations in the half-space. Journal of Functional Analysis, Elsevier, 2009, 256 (3), pp.881--927. ⟨10.1016/j.jfa.2008.11.019⟩. ⟨hal-00693056⟩

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