Courses
About the regularity in 3D incompressible Navier-Stokes equations: some classical and some recent results 4/4
Speaker: Jean-Yves Chemin (Université Claude-Bernard Lyon)Date: Friday, 13 March 2026 - 11:30-13:30Place: Aula Naranja, ICMAT
Abstract:
The purpose of this series of lectures is to give an overview (neccessarily partial) about the regularity problem for the homogeneous incompressible Navier-Stokes system in the whole space~$\R^3$. We try to make the proofs as self contained as possible for advances students. The required background is classical functional analysis including Young inequalities, Fourier transform and Sobolev inequalities.
Fourth lecture (13th of March)
In the last lecture lecture, we study the analytic smoothing effect regularity properties of the regular solution when the initial data is in a Sobolev spaces modeled on~$L^2$. Then we use this effect to construct an explicit function~$\Phi(t)$ on the maximal times of interval such that the radius of analyticity in bigger than~$1/\Phi(t)$. In the case when the solution remains bounded in some scaling invariant spaces, we obtain refined estimate of the solution up to the possible blow-up.
