Global large, smooth solutions of the 2D surface quasi-geostrophic equations

Abstract

In this paper, we prove the global regularity of smooth solutions to 2D surface quasi-geostrophic (SQG) equations with super-critical dissipation for a class of large initial data, where the velocity and temperature can be arbitrarily large in spaces $L^{\infty }({\mathbb{R}}^2)$ and $H^3({\mathbb{R}}^2)$. This result could be seen as an improvement work of Liu-Pan-Wu \cite{Liu}, for it's without any smallness hypothesis of the $L^{\infty }({\mathbb{R}}^2)$ norm of the initial data.

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References in corpus (4)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation
• Structure of Helicity and Global Solutions of Incompressible Navier-Stokes Equation
• A class large solution of the 2D MHD equations with velocity and magnetic damping

Cited by in corpus (1)

• On 3D Hall-MHD equations with fractional Laplacians: global well-posedness