Theoretical study of a Bénard Marangoni problem

[EN] In this paper we prove the existence of strong solutions for the stationary Benard-Marangoni problem in a finite domain flat on the top, bifurcating from the basic heat conductive state. The Benard-Marangoni problem is a physical phenomenon of thermal convection in which the effects of buoyancy and surface tension are taken into account. This problem is modelled with a system of partial differential equations of the type Navier-Stokes and heat equation. The boundary conditions include crossed boundary conditions involving tangential derivatives of the temperature and normal derivatives of the velocity field. To define tangential derivatives at the boundary, intended in the trace sense,…