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arXiv · 0806.4084

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

R. Danchin·M. Paicu
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Abstract

This paper is devoted to the study of the Cauchy problem for the Boussinesq system with partial viscosity in dimension $N\geq3.$ 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 {\it 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.

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R. Danchin, M. Paicu. 2008-06-25. Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces. https://doi.org/10.1016/j.physd.2008.03.034

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