| Private Homepage | http://www.uni-muenster.de/AMM/en/seis/ |
| Topics in Mathematics Münster | T5: Curvature, shape, and global analysis T6: Singularities and PDEs T9: Multi-scale processes and effective behaviour |
| Current Publications | • Meyer, David; Seis, Christian Propagation of regularity for transport equations. A Littlewood-Paley approach. Indiana University Mathematics Journal Vol. 73 (2), 2024 online • Ceci, Stefano; Seis, Christian On the dynamics of vortices in viscous 2D flows. Mathematische Annalen Vol. 388, 2024 online • Seis, Christian; Winkler, Dominik Invariant Manifolds for the Thin Film Equation. Archive for Rational Mechanics and Analysis Vol. 248 (2), 2024 online • Choi, Beomjun; Seis, Christian Finite-dimensional leading order dynamics for the fast diffusion equation near extinction. Discrete and Continuous Dynamical Systems - Series A Vol. 44 (9), 2024 online • Seis, Christian; Winkler, Dominik Fine large-time asymptotics for the axisymmetric Navier-Stokes equations. Journal of Evolution Equations Vol. 24, 2024 online • Seis, Christian; Winkler, Dominik Stability of traveling waves for doubly nonlinear equations. , 2024 online • Meyer, David; Seis, Christian Steady ring-shaped vortex sheets. , 2024 online • Choi, Beomjun; McCann, Robert J.; Seis, Christian Asymptotics near extinction for nonlinear fast diffusion on a bounded domain. Archive for Rational Mechanics and Analysis Vol. 247, 2023 online • Beck, Lisa; Cinti; Eleonora; Seis, Christian Optimal regularity of isoperimetric sets with Hölder densities. Calculus of Variations and Partial Differential Equations Vol. 62 (214), 2023 online |
| Current Projects | • Mathematical analysis of bubble rings in ideal fluids In this project, the evolution of toroidal bubble vortices is to be investigated. Bubble vortices are special vortices that occur in two-phase fluids. A typical and fascinating example is an air bubble ring in water created by dolphins or beluga whales. The underlying mathematical model is given by the two-phase Euler equations with surface tension. One major goal is a thorough mathematical construction of steady rings that move without changing their shape, and of perturbations of these. Such traveling waves are known for the classical Euler equations, but their existence is unknown for surface tension dependent models. Of particular interest is the role of the surface tension for the shape of the ring, which will be investigated. A second objective of this project is to understand how the effect of surface tension can be exploited to rigorously justify certain nonlinear motion laws of one or more interacting bubble rings. The understanding of such motion laws for the classical Euler equations is poor, and it is expected that the regularising effect of surface tension helps to mathematically tame the problem. • EXC 2044 - C1: Evolution and asymptotics In this unit, we will use generalisations of optimal transport metrics to develop gradient flow descriptions of (cross)-diffusion-reaction systems, rigorously analyse their pattern forming properties, and develop corresponding efficient numerical schemes. Related transport-type- and hyperbolic systems will be compared with respect to their pattern-forming behaviour, especially when mass is conserved. Bifurcations and the effects of noise perturbations will be explored. Moreover, we aim to understand defect structures, their stability and their interactions. Examples are the evolution of fractures in brittle materials and of vortices in fluids. Our analysis will explore the underlying geometry of defect dynamics such as gradient descents or Hamiltonian structures. Also, we will further develop continuum mechanics and asymptotic descriptions for multiple bodies which deform, divide, move, and dynamically attach to each other in order to better describe the bio-mechanics of growing and dividing soft tissues. Finally, we are interested in the asymptotic analysis of various random structures as the size or the dimension of the structure goes to infinity. More specifically, we shall consider random polytopes and random trees.For random polytopes we would like to compute the expected number of faces in all dimensions, the expected (intrinsic) volume, and absorption probabilities, as well as higher moments and limit distributions for these quantities. online • EXC 2044 - C2: Multi-scale phenomena and macroscopic structures In multi-scale problems, geometry and dynamics on the micro-scale influence structures on coarser scales. In this research unit we will investigate and analyse such structural interdependence based on topological, geometrical or dynamical properties of the underlying processes. We are interested in transport-dominated processes, such as in the problem of how efficient a fluid can be stirred to enhance mixing, and in the related analytical questions. A major concern will be the role of molecular diffusion and its interplay with the stirring process. High Péclet number flow in porous media with reaction at the surface of the porous material will be studied. Here, the flowinduces pore-scale fluctuations that lead to macroscopic enhanced diffusion and reaction kinetics. We also aim at understanding advection-dominated homogenisation problems in random regimes. We aim at classifying micro-scale geometry or topology with respect to the macroscopic behaviour of processes considered therein. Examples are meta material modelling and the analysis of processes in biological material. Motivated by network formation and fracture mechanics in random media, we will analyse the effective behaviour of curve and free-discontinuity energies with stochastic inhomogeneity. Furthermore, we are interested in adaptive algorithms that can balance the various design parameters arising in multi-scale methods. The analysis of such algorithms will be the key towards an optimal distribution of computational resources for multi-scale problems. Finally, we will study multi-scale energy landscapes and analyse asymptotic behaviour of hierarchical patterns occurring in variational models for transportation networks and related optimal transport problems. In particular, we will treat questions of self-similarity, cost distribution, and locality of the fine-scale pattern. We will establish new multilevel stochastic approximation algorithms with the aim of numerical optimisation in high dimensions. online | seis@uni-muenster.de |
| Phone | +49 251 83-35142 |
| FAX | +49 251 83-32729 |
| Room | 120.027 |
| Secretary | Sekretariat Claudia Giesbert Frau Claudia Giesbert Telefon +49 251 83-33792 Fax +49 251 83-32729 Zimmer 120.002 |
| Address | Prof. Dr. Christian Seis Angewandte Mathematik Münster: Institut für Analysis und Numerik Fachbereich Mathematik und Informatik der Universität Münster Orléans-Ring 10 48149 Münster |
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