Communications in Mathematical Sciences

Volume 15 (2017)

Number 4

Local well-posedness for the Bénard convection without surface tension

Pages: 903 – 956



Yunrui Zheng (Beijing International Center for Mathematical Research, Peking University, China)


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

Published 16 May 2017