© AG Seis

Analysis and PDEs

Institute for Analysis and Numerics
University of Münster


Office: Orléansring 10, 48149 Münster
Mail addess: Einsteinstr. 62, 48149 Münster
New Publication

Stefano Ceci's and my work on the motion of vortices in ideal fluids has been published in the Philosophical Transactions of the Royal Society A. Founded in 1665, this is the oldest scientific journal published in English. Our paper belongs to a theme issue entitled "Mathematical problems in physical fluid dynamics".

New Preprint

It is known that the transport equation with Sobolev velocity fields has poor regularity properties: Solutions may propagate only derivatives of logarithmic order. In a new work with David Meyer, we approach this problem with the help of Littlewood-Paley theory, which deals with a decomposition of the solution into dyadic frequency blocks. Our results have implications on mixing rates, rates of enhanced dissipation and on the zero-diffusivity-limit. The preprint is available here: https://arxiv.org/abs/2203.10860.

New Preprint

In a joint work with Stefano Ceci, I have investigated the motion of vorticity fields in two-dimensional viscous fluids. Our results show the optimal rates of spreading of vortex regions due to viscosity. This is a neat improvement on the existing literature. The motion of the vortices itself was predicted by Helmholtz in 1858! Here's the preprint: https://arxiv.org/abs/2203.07185.

Summer School in Ulm

I am honored to have been invited as a mini course speaker at the Summer School Horizons in non-linear PDEs in Ulm.

New Preprint

In a joint work with Beomjun Choi and Robert McCann I have investigated the fast diffusion equation on a bounded domain. In this model, the diffusivity becomes singular at the domain boundary, over which the mass escapes completely in finite time.  We show a nice dichotomy for the extinction rates in rescaled variables: The rate is either exponentially fast (with a rate constant predicted by the spectral gap), or algebraically slow. Here is a link to the preprint: https://arxiv.org/abs/2202.02769

New Preprint

Víctor Navarro-Fernández and André Schlichting have finished a new work on optimal error bounds for finite volume discretizations of advection-diffusion equations with rough coefficients. They prove that the numerical error cannot be larger than the order of the mesh size, which is much better than the purely advective case. Here is a link to the paper: https://arxiv.org/abs/2201.10411.

New focus in reading seminar

We resume our reading seminar. We start the year with a focus on Random Dynamical Systems. You can find more information on this webpage under Advanced Topics in ANALYSIS & PDEs.