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

By Raphaël Danchin, Marius Paicu. 2008

116 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/09be3bb58ab4c1215eae9227dd52465c3bef6fc1

Citations in the corpus

• Global regularity for the 2D anisotropic Boussinesq Equations with vertical dissipation (2011, unknown): “Other interesting recent results on the 2D Boussinesq equations can be found in [1, 2, 3, 11, 12, 15, 16, 24].”
• Global regularity results for the 2D Boussinesq equations with vertical dissipation (2011, unknown): “Other interesting recent results on the 2D Boussinesq equations can be found in [1,9,10,12,13, 17,20,22].”