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Danchin, Raphaël; Paicu, Marius
Global existence results for the anisotropic Boussinesq system in dimension two. (English) Zbl 1223.35249
Math. Models Methods Appl. Sci. 21, No. 3, 421-457 (2011).
This paper is a step forward concerning the analysis of a Boussinesq system in 2D, when the diffusivity and viscosity are variable only in horizontal direction and act in only one equation. This model is related with geophysical flows. In contrast with previous papers in the field, the present results are concerning the use of a vertical buoyancy force. Global weak solutions are considered, and existence and uniqueness theorems are obtained, assuming initial velocity in \(H^1\) and initial temperature in \(L^2\), by using the Friedrichs method. Some very interesting inequalities given in the appendix are used to get a priori estimates of the solution.
Reviewer: Gelu Paşa (Bucureşti)

Cited in 1 Review
Cited in 93 Documents
MSC:
35Q30 Navier-Stokes equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35D30 Weak solutions to PDEs
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76U05 General theory of rotating fluids
86A04 General questions in geophysics
Keywords:
Boussinesq system; geophysical flows; convection; turbulent viscosity; anisotrpic
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\textit{R. Danchin} and \textit{M. Paicu}, Math. Models Methods Appl. Sci. 21, No. 3, 421--457 (2011; Zbl 1223.35249)
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