an:05908847
Zbl 1223.35249
Danchin, Rapha??l; Paicu, Marius
Global existence results for the anisotropic Boussinesq system in dimension two
EN
Math. Models Methods Appl. Sci. 21, No. 3, 421-457 (2011).
00277371
2011
j
35Q30 35B30 35D30 76D03 76U05 86A04
Boussinesq system; geophysical flows; convection; turbulent viscosity; anisotrpic
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.
Gelu Pa??a (Bucure??ti)