Communications in Mathematical Sciences
Volume 15 (2017)
Local well-posedness for the Bénard convection without surface tension
Pages: 903 – 956
We consider the Bénard convection in a three-dimensional domain bounded below by a fixed flatten boundary and above by a free moving surface. The domain is horizontally periodic. The fluid dynamics are governed by the Boussinesq approximation and the effect of surface tension is neglected on the free surface. Here we develop a local well-posedness theory for the equations of general case in the framework of the nonlinear energy method.
free boundary problems, incompressible viscous fluids, Bénard convection
2010 Mathematics Subject Classification
35Q30, 35R35, 76E06