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Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces

Abstract : This paper is devoted to the study of the Cauchy problem for the Boussinesq system with partial viscosity in dimension N >= 3. First we prove a global existence result for data in Lorentz spaces satisfying a smallness condition which is at the scaling of the equations. Second, we get a uniqueness result in Besov spaces with negative indices of regularity (despite the fact that there is no smoothing effect on the temperature). The proof relies on a priori estimates with loss of regularity for the nonstationary Stokes system with convection. As a corollary, we obtain a global existence and uniqueness result for small data in Lorentz spaces. (c) 2008 Elsevier B.V. All rights reserved.
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Submitted on : Tuesday, May 1, 2012 - 7:53:24 PM
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Raphaël Danchin, Marius Paicu. Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces. Physica D: Nonlinear Phenomena, Elsevier, 2008, 237 (10-12), pp.1444--1460. ⟨10.1016/j.physd.2008.03.034⟩. ⟨hal-00693065⟩

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