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The Leray and Fujita-Kato theorems for the Boussinesq system with partial viscosity. (Les théorèmes de Leray et de Fujita-Kato pour le système de Boussinesqpartiellement visqueux.) (English) Zbl 1162.35063
The paper is concerned with the study of the global existence of finite energy weak solutions in any dimension, of the uniqueness of the finite energy global solutions in two-dimensional case and with the study of the global well-posedness in dimension \(N\geq 3\) of a Boussinesq system for small data.

MSC:
35Q35 PDEs in connection with fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35B65 Smoothness and regularity of solutions to PDEs
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