This paper aims to give a detailed presentation of long-wave instabilities of shear layers for NavierStokes equations,and in particular to give a simple and easy-to-read presentation of the study of the OrrSommerfeld ...This paper aims to give a detailed presentation of long-wave instabilities of shear layers for NavierStokes equations,and in particular to give a simple and easy-to-read presentation of the study of the OrrSommerfeld equation and to detail the analysis of its adjoint.Using these analyses,we prove the existence of long-wave instabilities in the cases of slowly rotating fuids,slightly compressible fuids,or fuids with Navier boundary conditions,under smallness conditions.展开更多
The Rayleigh-B^nard convection is a classical problem in fluid dynamics. In this paper, we are concerned with the well-posedness for the compressible Rayleigh-B^nard convection in a bounded domain Ω R2. We prove the...The Rayleigh-B^nard convection is a classical problem in fluid dynamics. In this paper, we are concerned with the well-posedness for the compressible Rayleigh-B^nard convection in a bounded domain Ω R2. We prove the local well-posedness of the system with appropriate initial data. This is the result concerning compressible Rayleigh-B^nard convection, before only results about incompressible Rayleigh-B^nard convection were done.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11871005 and 12271032)。
文摘This paper aims to give a detailed presentation of long-wave instabilities of shear layers for NavierStokes equations,and in particular to give a simple and easy-to-read presentation of the study of the OrrSommerfeld equation and to detail the analysis of its adjoint.Using these analyses,we prove the existence of long-wave instabilities in the cases of slowly rotating fuids,slightly compressible fuids,or fuids with Navier boundary conditions,under smallness conditions.
文摘The Rayleigh-B^nard convection is a classical problem in fluid dynamics. In this paper, we are concerned with the well-posedness for the compressible Rayleigh-B^nard convection in a bounded domain Ω R2. We prove the local well-posedness of the system with appropriate initial data. This is the result concerning compressible Rayleigh-B^nard convection, before only results about incompressible Rayleigh-B^nard convection were done.
