Théorie de Littlewood-Paley et application aux EDP (Partie 1/2)

Orateur: Timothée CRIN-BARAT
Type: Séminaire des doctorants
Site: UPEC
Salle: Salle P3 413
Date de début: 12/11/2019 - 14:00
Date de fin: 12/11/2019 - 15:30

The basic idea of the Littlewood-Paley Theory consists in a localization procedure in the frequency space. The interest of this method is that the derivatives (or more generally the Fourier multipliers) act in a very special way on distributions which Fourier transform is supported in a ball or a ring.
To explain this, I will first present and prove the Bernstein's Lemma. From this lemma we will define a specific dyadic partition of unity that will be the main tool to construct the Besov spaces. I will then give you multiple properties of those spaces and especially about the paradifferential calculus that turns out to be very useful in the study of PDE.
I will then give some examples of why those spaces are useful in the theory of PDEs.