Seminar Analysis and Mathematical Physics: Luis Martinez Zoroa (ICMAT Madrid)

Instantaneous loss of regularity for SQG with fractional diffusion

The Surface quasi-geostrophic (SQG) equation is an important active scalar model, both due to its shared properties with 3D Euler as well as for its applications to model certain atmospherical phenomena. It has already been established that instantaneous loss of regularity can occur in the inviscid case in certain Sobolev spaces, but it is unclear at what point the diffusion prevents this phenomenon from happening. In this talk I will discuss the behaviour when there is some super-critical fractional diffusion.

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