On the global well-posedness of a class of Boussinesq- Navier-Stokes systems

Abstract

In this paper we consider the following 2D Boussinesq-Navier-Stokes systems \partial_{t}u+u\cdot\nabla u+\nabla p+ |D|^αu &= θe_{2} \partial_{t}θ+u\cdot\nabla θ+ |D|^βθ&=0 \quad with $\text{div}u=0$ and $0<\beta <\alpha <1$. When $\frac{6-\sqrt{6}}{4}<\alpha <1$, $1-\alpha <\beta \le f(\alpha )$, where $f(\alpha )$ is an explicit function as a technical bound, we prove global well-posedness results for rough initial data.

arXiv comment23pages

References in corpus (2)

• A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation
• Global well-posedness of the critical Burgers equation in critical Besov spaces

Cited by in corpus (3)

• On the global well-posedness for the Boussinesq system with horizontal dissipation
• Global well-posedness for axisymmetric Boussinesq system with horizontal viscosity
• Global well-posedness of the 2D Boussinesq equations with fractional Laplacian dissipation