Scaling and criticality in stochastic evolution equations

Agresti Antonio, TU Delft

Scaling and criticality have always played a pivotal role in understanding fundamental properties of solutions to a given (stochastic) PDE. Its relevance is well-known in fluid dynamics, where scaling invariant (i.e. critical) spaces have nowadays become cornerstone tools for studying Navier-Stokes equations. Recently, in the context of (stochastic) evolution equations, a more systematic treatment and comprehensive theory for treating critical spaces have been developed. The aim of this talk is to discuss the basic features of the latter, and its connections with the $L^q$-theory of SPDEs with $q\gg 2$ pioneered by N.V. Krylov. We will explain the wide reach of this theory by means of its application to reaction-diffusion equations with transport noise, which arise in several physical and engineering applications such as chemical reactions and population dynamics where stochasticity models turbulent phenomena. Based on joint works with M. Veraar (TU Delft).

Area: CS16 - Stochastic Evolution Equations (Irene Benedetti)

Keywords: Critical spaces, scaling, transport noise

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