# Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

### Sharp Fronts for the SQG Equation

**PDE and Applied Math Seminar**

Speaker: | Jingyang Shu, Temple University |

Location: | ZOOM |

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.