Stochastic fluid dynamics: many phenomena in fluid dynamics cannot be described by purely deterministic models; probability gives phenomenological models aand interpretation to better understand these phenomena. I have worked on:
Kraichnan model of passive scalars
Vortices on 2D domains with boundaries
Stochastic 2D Euler equations with transport noise
Geometric viewpoing on stochastic PDEs
Regularization by noise: given an ill-posed ODE or PDE, we can sometimes recover well-posedness and better regularity by the addition of a (rough!) random noise term. I have worked on:
Regularization for stochastic ODEs and related linear stochastic PDEs
Regularization for some nonlinear PDEs
Regularization for 2D Euler equations and other fluid dynamic PDEs
No blow up by noise
Zero noise selection problem
McKean-Vlasov stochastic ODEs and related interacting particle systems: interacting particles with so-called mean field interaction, in the limit of high particle number, are better described by a single, distribution-dependent stochastic ODE. I have worked on:
Singular interaction case
McKean-Vlasov equations with reflection
Pathwise approach
Applications
Other topics:
Models for sulphation in monuments
My publications are available on Google Scholar and ORCID .
Most of my preprints are available on arXiv .
Here you find my CV with a list of publications.