Courses
About the regularity in 3D incompressible Navier-Stokes equations: some classical and some recent results 2/4
Speaker: Jean-Yves Chemin (Université Claude-Bernard Lyon)Date: Wednesday, 11 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.
Second lecture (11th of March)
In the second lecture, we interpret the result of wellposedness for initial data in the Lebesgue spaces $L^3$ in term of Besov spaces of negative index. We state and comment the celebrated end-point theorem of Koch and Tataru, omitting the proof because of the lack of time.
Then we revisit wellposedness results for Besov space of negative index using Littlewood-Paley theory.
