Well-posedness for compressible Rayleigh-Benard convection

摘要

The Rayleigh-Benard convection is a classical problem in fluid dynamics. In this paper, we are concerned with the well-posedness for the compressible Rayleigh-Benard convection in a bounded domain Ω C R~2. We prove the local well-posedness of the system with appropriate initial data. This is the result concerning compressible Rayleigh-Benard convection, before only results about incompressible Rayleigh-Benard convection were done.