English

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

Analysis of PDEs 2018-05-23 v2

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.

Keywords

Cite

@article{arxiv.1709.03194,
  title  = {Regularized and Approximate Equations for Sharp Fronts in the Surface Quasi-Geostrophic Equation and its Generalizations},
  author = {John K. Hunter and Jingyang Shu},
  journal= {arXiv preprint arXiv:1709.03194},
  year   = {2018}
}
R2 v1 2026-06-22T21:38:31.952Z