Fourier Analysis Methods for Evolutionary Partial Differential Equations

Speaker(s)

Prof. Raphaela Danchina

Date

March 20, 2014, noon

Room

room 3130

Seminar

Seminar of Mathematical Physics Equations Group

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Fourier analysis methods have known a growing importance recently in the study of linear and nonlinear PDE's. In particular, techniques based on Littlewood-Paley decomposition and paradifferential calculus have proved to be very efficient for tackling problems in the whole space or in the torus. In these lectures, we aim at presenting those techniques, having in mind to solve classical systems of equations arising in fluid mechanics. We shall in particular prove the existence and uniqueness of strong solutions for the incompressible and the compressible Navier-Stokes equations in so-called critical functional spaces. In passing, we shall provide a bunch of useful estimates for linear equations: heat, transport, Schrödinger and so on.

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