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


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.