© AG Seis

Research group

Analysis and PDEs

Prof. Dr. Christian Seis

Institute for Analysis and Numerics
University of Münster

Office: Orléans-Ring 10, 48149 Münster

Mail addess: Einsteinstr. 62, 48149 Münster

What's going on??
Welcome to our news blog
| Workshop Mixing, Stability and Fluid Dynamics
© MM/V Liesche

This week our mini-workshop on Mixing and stability properties in fluid dynamics took place. A timely theme! We had interesting talks and inspiring discussions about new developments and long-standing questions.

| New preprint

In a joint work with Lisa Beck and Eleonora Cinti, I have studied the optimal regularity of isoperimetric sets in the case where the perimeter functional and the volume have both a Hölder weight. The preprint is on the arXiv.

| New group member

Lukas Niebel joined our working group on April 1st. In May he will defend his dissertation thesis on regularity estimates for kinetic equations at the University of Ulm. He will assist us in studying vortex rings in ideal fluids. Welcome Lukas!

| New Publication

My joint work with Stefano Ceci on point vortex dynamics in viscous fluids has been published in the journal Mathematische Annalen.

| X-mas Seminar
© V Navarro Fernandez

In our last meeting this year, we had eight talks on our own current research. It was a nice event with cookies, pizza and hot wine. Here is a new group foto, on which four persons are missing...

| New publication

After having waited for the reviews for almost 2 years, my paper on bounds on the rates of enhanced dissipation was finally published in Communications in Mathematical Physics. Uff...

| New Preprint

Together with my PhD student Dominik Winkler I investigate the large time asymptotics for solutions to a thin film equation. We achieve this by constructing invariant manifolds near the self-similar solution. Here's the preprint: https://arxiv.org/abs/2212.02262.

| Reading Seminar Update

After having studied Random Dynamical Systems in our reading seminar Advanced Topics in ANALYSIS & PDEs for about ten months, we return to the deterministic setting and read Villani's monograph on hypocoercivity.

| Visiting Doctoral Researcher

I am very happy that Nicola De Nitti from FAU Erlangen-Nürnberg joins us for a 2-months period. Nicola's stay is funded by the Cluster of Excellence as part of a guest program for young scientists.

| Public Science Festival

I was invited to give a lecture at the public science festival Schlauraum in Münster. I chose to speak about The Mathematics of turbulent flows and the search for a million dollars.

| 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.