Unified theory on V-states structures for active scalar equations

SEMINARIO DE ECUACIONES DIFERENCIALES

Conferenciante: Zhilong Xue (Beijing Normal University)

Abstract: In this talk, we will first introduce some recent results about patch solutions for active scaler equation, including two dimensional Euler equation. Then we will present how to establish the existence of simply connected V-states (rotating patches) close to Rankine vortices for active scalar equations with completely monotone kernels. This result allows to unify various results on this topic related to geophysical flows. A key ingredient is a new factorization formula for the spectrum using a universal function which is independent of the model. This function admits sesveral interesting properties allowing to track the spectrum distribution. This talk is based on a joint work with Taoufik Hmidi and Liutang Xue.

Seminario de Ecuaciones Diferenciales: https://www.ugr.es/~sed/