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April Colloquium

Apr 20, 2023

****Dirk Peschka (WIAS / FU Berlin)
Title: Multiscale limits of thin-film models with moving support

In this talk, we will be exploring some intriguing features of thin-film models. Despite their simple appearance, these models have proven to be both mathematically challenging to analyze and physically sensible for predicting flows of viscous fluids with free boundaries. These degenerate fourth-order equations exhibit a gradient flow structure and have a rich structure of possible structure formation process.

In order to address a broader audience in the CRC, I will first give an introduction to the underlying variational structures and show how one can develop numerical methods systematically and provide some generally relevant examples.


****Richard Schubert (Universität Bonn)
Title: Sedimentation of Particles with Small Inertia in Stokes Flow

Abstract: We discuss the derivation of macroscopic equations for the description of particulate flows, in particular sedimentation. We will assume that the particles are spherical and derive mean-field limits as the number of the particles tends to infinity and their inertia tends to zero.
We show that the particle evolution is approximated in Wasserstein distance by the transport-Stokes system which has been derived previously as the mean-field limit of inertialess particles. In particular this justifies to neglect the particle inertia in the microscopic system, which is a typical modelling assumption in this and related contexts.
Moreover, we show that the particle evolution is approximated with a smaller error by the Vlasov-Stokes equations that take into account the particle inertia. This can be regarded as a first step in the yet open derivation of the Navier-Stokes-Vlasov equations.
This is joint work with Richard Höfer (Regensburg.)


****Carolin Mehlmann (Otto-von-Guericke-Universität Magdeburg)
Title: Mathematical modeling of sea ice dynamics: recent advances and open questions

Subject of this talk are the mathematical challenges and the numerical treatment of large scale sea ice problems. The model under consideration goes back to Hibler (”A dynamic thermodynamic sea ice model”, J. Phys. Oceanogr., Hibler 1979) and is based on a viscous-plastic description of the ice as a two-dimensional thin layer on the ocean surface.

In the first part of this talk we discuss the model in order to find a suitable presentation for applying numerical analysis and modern approximation techniques. The second part focuses on the presentation of new numerical methods to discretize the strongly nonlinear equation in space. In last part of the talk we discuss the limits of the model and outline new particle-continuum approach to improve the representation of sea ice in climate models.