Mathematics Colloquia and Seminars
Sharp Fronts for the SQG EquationPDE and Applied Math Seminar
|Speaker:||Jingyang Shu, Temple University|
|Start time:||Fri, May 1 2020, 4:10PM|
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 solutions exist and are global. For two SQG fronts, the contour dynamics equations form a system with more complicated dispersion relations as well as quadratic nonlinearities. Numerical simulations for front solutions suggest the formation of finite-time singularity. This is joint work with John K. Hunter and Qingtian Zhang.