Local wellposedness of an approximate equation for SQG fronts

Abstract

We prove local well-posedness in the Sobolev spaces ${\dot{H}}^s(\mathbb{T})$, with $s>7/2$, for an initial value problem for a nonlocal, cubically nonlinear, dispersive equation that provides an approximate description of the evolution of surface quasi-geostrophic (SQG) fronts with small slopes.

18 pages, 1 figure

References in corpus (1)

• Regularized and Approximate Equations for Sharp Fronts in the Surface Quasi-Geostrophic Equation and its Generalizations

Cited by in corpus (1)

• Global Solutions of a Surface Quasi-Geostrophic Front Equation