*Online Conference* Analysis of Fluids and Related Topics: Sharp Fronts for the SQG Equation, Speaker: Jingyang Shu, University of California, Davis

Analysis of Fluids and Related Topics
  • Jingyang Shu
  • University of California, Davis
  • Sharp Fronts for the SQG Equation
May 7, 2020
4:30 pm
*Online Conference*

 Jingyang Shu, University of California, Davis

Zoom link:   https://princeton.zoom.us/j/9148065146

Piecewise-constant fronts of the surface quasi-geostrophic (SQG) equation support surface waves. For planar SQG fronts, the formal contour dynamics equation does not converge. We use a decomposition method to overcome this difficulty and obtain a well-formulated meaningful contour dynamics equation for fronts that are described as a graph. The resulting equation is a nonlocal quasi-linear equation with logarithmic dispersion. With smallness and smoothness assumptions on the initial data, the front equation admits global solutions. For two SQG fronts, the contour dynamics equations form a system with more complicated dispersion relations as well as nonlinear interactions between the two fronts. Numerical simulations for front solutions suggest the formation of finite-time singularity. This is joint work with John K. Hunter and Qingtian Zhang.