Global regularity for the viscous Boussinesq equations
نویسندگان
چکیده
منابع مشابه
Global regularity for the viscous Boussinesq equations
∇·u=0 Here is the temperature, u=(u1; u2) is the velocity, p is the pressure. In Reference [1], Pumir and Siggia observed that the cap of a symmetric rising bubble collapses in a nite time. In contrast, E and Shu [2] reported that the motion of the bubble cap is a very unlikely candidate for nite time singularity formation. In this paper, we prove the global regularity for the viscous Boussines...
متن کاملGlobal Well-posedness of the Viscous Boussinesq Equations
We prove the global well-posedness of the viscous incompressible Boussinesq equations in two spatial dimensions for general initial data in Hm with m ≥ 3. It is known that when both the velocity and the density equations have finite positive viscosity, the Boussinesq system does not develop finite time singularities. We consider here the challenging case when viscosity enters only in the veloci...
متن کاملAn Osgood Type Regularity Criterion for the 3D Boussinesq Equations
We consider the three-dimensional Boussinesq equations, and obtain an Osgood type regularity criterion in terms of the velocity gradient.
متن کاملRegularity Criteria for the 2d Boussinesq Equations with Supercritical Dissipation∗
This paper focuses on the 2D incompressible Boussinesq equations with fractional dissipation, given by Λαu in the velocity equation and by Λβθ in the temperature equation, where Λ= √−Δ denotes the Zygmund operator. Due to the vortex stretching and the lack of sufficient dissipation, the global regularity problem for the supercritical regime α+β<1 remains an outstanding problem. This paper prese...
متن کاملGlobal regularity for the 2D Boussinesq equations with partial viscosity terms
In this paper we prove the global in time regularity for the 2D Boussinesq system with either the zero diffusivity or the zero viscosity. We also prove that as diffusivity(viscosity) goes to zero the solutions of the fully viscous equations converges stongly to those of zero diffusion(viscosity) equations. Our result for the zero diffusion system, in particular, solves the Problem no. 3 posed b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Methods in the Applied Sciences
سال: 2004
ISSN: 0170-4214
DOI: 10.1002/mma.457