## Event Date:

## Event Location:

- 4607B South Hall

## Event Price:

Free

## Event Contact:

Carlos Garcia-Cervera

Email: cgarcia@math.ucsb.edu

Phone: 8055638873

- Applied Math/PDE Seminar

Magnetic materials have the special property that they react to applied external fields in remarkable ways and have therefore many technological applications. They can not only be found in medical applications, but, for example, also in loud speakers and shock absorbers.

We propose a model for micromagnetic materials in the framework of complex fluids. The system of PDEs to model the flow of the material is derived in a continuum mechanical setting from variational principles including the least action principle and the maximum dissipation principle. In this talk, we outline the process of modeling and the energetic variational approach. Moreover, we highlight the coupling between the elastic and the magnetic properties of the material.

The obtained model is a very general model of micromagnetic materials, but, on the other hand, seems to be rather complex from the analytical point of view. Therefore, we provide also a simplified version of the model that is amenable for analysis but applies only to some particular flow regimes. As an illustration, we will concentrate on the two dimensionsional case where an explicit ansatz for the solution of the magnetization can be found. With this ansatz we simplify the model even further and show existence of weak solutions.

This is joint work with Barbora Benev{s}ov'{a} (Institute for Mathematics, University of W"urzburg, Germany), Carlos Garc{'i}a-Cervera (Mathematics Department, University of California, Santa Barbara, USA), Chun Liu (Department of Mathematics, Penn State University, University Park, USA), and Anja Schl"omerkemper (Institute for Mathematics, University of W"urzburg, Germany).