Global Solutions of a Surface Quasi-Geostrophic Front Equation

Abstract

We consider a nonlinear, spatially-nonlocal initial value problem in one space dimension on $\mathbb{R}$ that describes the motion of surface quasi-geostrophic (SQG) fronts. We prove that the initial value problem has a unique local smooth solution under a convergence condition on the multilinear expansion of the nonlinear term in the equation, and, for sufficiently smooth and small initial data, we prove that the solution is global.

55 pages

References in corpus (7)

• On Kato-Ponce and fractional Leibniz
• The Euler--Maxwell system for electrons: global solutions in $2D$
• A direct approach to nonuniqueness and failure of compactness for the SQG equation
• Regularized and Approximate Equations for Sharp Fronts in the Surface Quasi-Geostrophic Equation and its Generalizations
• Contour Dynamics for Surface Quasi-Geostrophic Fronts
• Local wellposedness of an approximate equation for SQG fronts
• Global solutions for 2D quadratic Schrodinger equations

Cited by in corpus (5)

• Two-Front Solutions of the SQG Equation and its Generalizations
• Global solutions for a family of GSQG front equations
• The $\alpha$-SQG patch problem is illposed in $C^{2,\beta }$ and $W^{2,p}$
• On the approximation of vorticity fronts by the Burgers-Hilbert equation
• The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation