Seminarium KMMF "Teoria Dwoistości"

In this talk, I would like to present arguments explaining why theapproach based on Besov spaces provides some of the strongest results inthe analysis of systems of partial differential equations. I will focus ontheir fundamental properties and demonstrate how they can be effectivelyapplied to systems arising in fluid mechanics, in particular to theNavier–Stokes equations.I will also discuss a simple example related to the heat equation in orderto illustrate the relative simplicity and transparency of this approach.Alongside the basic definitions and properties of Besov spaces, I willoutline the main directions of development of this method, as well as itslimitations.The central role in this framework is played by Fourier analysis, whichprovides the most natural and intuitive description of Besov spaces andtheir structure.This will be a blackboard talk, and I will aim to keep close contact withthe audience throughout the presentation.