Abstract
The 2D incompressible Boussinesq system with partial or fractional dissipation have recently attracted considerable attention. In this paper, we study the Cauchy problem for the 2D Boussinesq system in a periodic domain with fractional vertical dissipation in the subcritical case, and we prove the global well-posedness of strong solutions. Based on this, we also discuss the existence of the global attractor.
Highlights
1 Introduction This paper studies the D incompressible Boussinesq system with fractional vertical dissipation
Huang [ ] addressed the well-posedness of the D (Euler)-Boussinesq equations with zero viscosity positive diffusivity in the polygonal-like domains with Yudovich’s type data and in [ ] proved the global well-posedness of strong solutions and existence of the global attractor to the initial and boundary value problem in a periodic channel with non-homogeneous boundary conditions for the temperature and viscosity and thermal diffusivity depending on the temperature
We prove the existence of global attractor for the solution operator S(t) to the Boussinesq system ( . ) in the space Hs × Hs, where s ≥
Summary
This paper studies the D incompressible Boussinesq system with fractional vertical dissipation. ). In the case when ν and κ are positive constants, Cannon and DiBenedetto [ ] studied the Cauchy problem for the Boussinesq system, and further proved the existence of a unique global in time weak solution. Pan and Zhang [ , ] proved the existence of a unique global smooth solution to the initial boundary value problem of D inviscid heat conductive Boussinesq equations with nonlinear heat diffusion over a bounded domain with smooth boundary.
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