On the global classical solutions for the generalized SQG equation

Abstract

In this paper, we study the existence of global classical solutions to the generalized surface quasi-geostrophic equation. By using the variational method, we provide some new families of global classical solutions for to the generalized surface quasigeostrophic equation. These solutions mainly consist of rotating solutions and travellingwave solutions.

On White Noise Solutions of mSQG Equations on $\mathbb{R}^{2}$

“…mSQG equations, which are equations between SQG equations and Euler equations, have also been studied by many papers, such as [13,14,4,11]. In a recent work [3], nontrivial global (classical) solutions of the mSQG equations have been constructed.…”