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

Abstract

We derive regularized contour dynamics equations for the motion of infinite sharp fronts in the two-dimensional incompressible Euler, surface quasi-geostrophic (SQG), and generalized surface quasi-geostrophic (gSQG) equations. We derive a cubic approximation of the contour dynamics equation and prove the short-time well-posedness of the approximate equations for generalized surface quasi-geostrophic fronts and weak well-posedness for surface quasi-geostrophic fronts.

Cited by in corpus (6)

• Global Solutions of a Surface Quasi-Geostrophic Front Equation
• Contour Dynamics for Surface Quasi-Geostrophic Fronts
• Local wellposedness of an approximate equation for SQG fronts
• Two-Front Solutions of the SQG Equation and its Generalizations
• Global solutions for a family of GSQG front equations
• On the approximation of vorticity fronts by the Burgers-Hilbert equation