Global Well-posedness for a Boussinesq- Navier-stokes System with Critical Dissipation
نویسنده
چکیده
In this paper we study a fractional diffusion Boussinesq model which couples a Navier-Stokes type equation with fractional diffusion for the velocity and a transport equation for the temperature. We establish global well-posedness results with rough initial data.
منابع مشابه
The 2d Boussinesq-navier-stokes Equations with Logarithmically Supercritical Dissipation
This paper studies the global well-posedness of the initial-value problem for the 2D Boussinesq-Navier-Stokes equations with dissipation given by an operator L that can be defined through both an integral kernel and a Fourier multiplier. When the symbol of L is represented by |ξ| a(|ξ|) with a satisfying lim|ξ|→∞ a(|ξ|) |ξ|σ = 0 for any σ > 0, we obtain the global well-posedness. A special cons...
متن کاملOn the Global Regularity of Axisymmetric Navier-stokes-boussinesq System
In this paper we prove a global well-posedness result for tridimensional Navier-Stokes-Boussinesq system with axisymmetric initial data. This system couples Navier-Stokes equations with a transport equation governing the density.
متن کاملOn the global well-posedness of a class of Boussinesq- Navier-Stokes systems
In this paper we consider the following 2D Boussinesq-Navier-Stokes systems ∂tu+ u · ∇u+∇p+ |D|u = θe2 ∂tθ + u · ∇θ + |D|θ = 0 with divu = 0 and 0 < β < α < 1. When 6− √ 6 4 < α < 1, 1−α < β ≤ f(α), where f(α) is an explicit function as a technical bound, we prove global well-posedness results for rough initial data. Mathematics Subject Classification (2000): 76D03, 76D05, 35B33, 35Q35
متن کاملGlobal Well-posedness for Euler-boussinesq System with Critical Dissipation
In this paper we study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.
متن کاملWell-posedness and Inviscid Limits of the Boussinesq Equations with Fractional Laplacian Dissipation
This paper is concerned with the global well-posedness and inviscid limits of several systems of Boussinesq equations with fractional dissipation. Three main results are proven. The first result assesses the global regularity of two systems of equations close to the critical 2D Boussinesq equations. This is achieved by examining their inviscid limits. The second result relates the global regula...
متن کامل