GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWOReport as inadecuate




GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO - Download this document for free, or read online. Document in PDF available to download.

1 LAMA - Laboratoire d-Analyse et de Mathématiques Appliquées 2 LM-Orsay - Laboratoire de Mathématiques d-Orsay

Abstract : We study the global existence issue for the two-dimensional Boussinesq system with horizontal viscosity in only one equation.
We first examine the case where the Navier-Stokes equation with no vertical viscosity is coupled with a transport equation.
Second, we consider a coupling between the classical two-dimensional incompressible Euler equation and a transportdiffusion equation with diffusion in the horizontal direction only.
For the both systems and for arbitrarily large data, we construct global weak solutions `a la Leray.
Next, we state global wellposedness results for more regular data.
Our results strongly rely on the fact that the diffusion occurs in a direction perpendicular to the buoyancy force.






Author: Raphaël Danchin - Marius Paicu -

Source: https://hal.archives-ouvertes.fr/



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