The Department of Mathematical Sciences will continue its free Math Seminar Series on Friday, February 22, at 11:20 a.m. in Armitage Hall, Room 121. Camillo De Lellis of the Institute of Advanced Study in Princeton, New Jersey will present, “Non-local Navier-Stokes equations.” 

The abstract of Dr. De Lellis’ talk is as follows:

I will consider a variant of the Navier-Stokes equations, where the classical Laplacian is substituted by a fractional Laplacian $-(-\Delta)^\alpha$. I will present two results. In the hypodissipative case, i.e. when $\alpha$ is sufficiently small, in a joint work with Maria Colombo and Luigi De Rosa we show that Leray solutions are ill-posed. In the hyperdissipative case, i.e. when $\alpha>1$, in a joint work with Maria Colombo and Annalisa Massaccesi we prove a “strong analog” of the Caffarelli-Kohn-Nirenberg Theorem, which strengthens the conclusions of a previous work by Katz and Pavlovic.