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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
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.
