# Seminario

#### Seminario EDPs y Mecánica de Fluidos

Non existence and strong ill-posedness in C^k and Sobolev spaces for SQG

Ponente:  Luis Martínez-Zoroa (ICMAT)
Fecha:  martes 05 de abril de 2022 - 12:00
Lugar:  Aula Naranja, ICMAT

Resumen:

We construct solutions in $${R}^2$$ with finite energy of the surface quasi-geostrophic equations (SQG) that initially are in $$C^k$$ ($$k\geq 2$$) but that are not in $$C^{k}$$ for $$t>0$$. We prove a similar result also for $$H^{s}$$ in the range $$s\in(\frac32,2)$$. Moreover, we prove strong ill-posedness in the critical space $$H^{2}$$.
Joint work with D. Cordoba.