## 2020

#### Professor Stefano Spirito, University of L'Aquila, Italy

*February 1st - February 15th*

Stefano Spirito, Assistant Professor, Department of Mathematics, University of L’Aquila, Italy

Tuesday, February 11, 2020, 15:00

- 16:00

Building 1, Level 3, Room 3119

##### Contact Person

In this talk we consider the Cauchy problem for the 2D Euler equations for incompressible inviscid fluids. It is well-known that given a smooth initial datum, the Cauchy problem is well-posed and in particular the energy is conserved and the vorticity is transported by the flow of the velocity. When we consider weak solutions this might not be the case anymore. We will review some recent results obtained in collaboration with Gianluca Crippa and Gennaro Ciampa where we extend those properties to the case of irregular vorticities. In particular, under low integrability assumptions on the vorticity we show that certain approximations important from a physical and a numerical point of view converge to solutions satisfying those properties.

#### Professor Dimitrios Mitsotakis, Victoria University of Wellington, New Zealand

*January 3rd - February 29th*

Dimitrios Mitsotakis, Senior Lecturer, School of Mathematics and Statistic Victoria University of Wellington, New Zealand

Wednesday, February 05, 2020, 16:00

- 17:00

Building 1, Level 4, Room 4214

##### Contact Person

In this talk we present the derivation of a new Boussinesq-type system to describe the propagation of long waves of small amplitude in a basin with mildly varying bottom topography. We prove the existence and uniqueness of weak solutions for maximal times that do not depend on the amplitude of the waves. We then present the numerical solution of the new system using Galerkin finite element methods and prove the convergence of the semidiscrete solution to the exact solution. The system appears to describe well water waves even in benchmark experiments that involve also general bathymetries.

## 2019

#### Professor Jan Giesselman, Technical University of Darmstadt, Germany

*April 1st - April 11th*

Prof. Jan Giesselmann, Technical University of Darmstadt, Germany

Tuesday, April 02, 2019, 16:00

- 17:00

B1 L3 Room 3119

##### Contact Person

In this course we consider multi-phase flows, i.e., flows of one substance which is present as liquid as well as vapor. We focus on models that resolve individual bubbles/droplets and that treat both phases as compressible. We will also discuss incompressible/low Mach limits, since in most applications the liquid is nearly incompressible. Understanding and simulating such small-scale models is important in order to obtain information which can be used in larger scale models for e.g. sprays which play important roles in processes of practical interest as diverse as combustion, chemical engineering, and cloud formation

#### Dr. Suleyman Ulusoy, American University of Ras Al Khaimah, UAE

*March 17th - March 22nd*

Dr. Suleyman Ulusoy, American University of Ras Al Khaimah, UAE

Wednesday, March 20, 2019, 16:00

- 17:00

Building 1, Level 3, Room 3119

##### Contact Person

In the first part of the talk we investigate a Keller-Segel model with quorum sensing and a fractional diffusion operator. This model describes the collective cell movement due to chemical sensing with flux limitation for high cell densities and with anomalous media represented by a nonlinear, degenerate fractional diffusion operator. The purpose here is to introduce and prove the existence of a properly defined entropy solution. In the second part of the talk we will analyze an equation that is gradient flow of a functional related to Hardy-Littlewood-Sobolev inequality in whole Euclidean space of higher dimensions.

#### Professor Dimitrios Mitsotakis, Victoria University of Wellington, New Zealand

*January 26th - March 2nd*

Dimitrios Mitsotakis, Victoria Univ. Wellington New Zealand

Sunday, February 10, 2019, 16:00

- 17:30

Building 1, Level 3, Room 3119

##### Contact Person

**Abstract : **The mathematical modelling of water waves continues to attract great interest bo