## Interaction of Deterministic or Stochastic Forces on Flat or Moving Interfaces

The evolution of a geophysical flow governed by the primitive equations in geometries with flat boundaries and homogeneous boundary data is rather well understood and the underlying equations are known to be strongly globally well-posed. This is no longer the case when deterministic or stochastic forces are applied or when the underlying domain is allowed to be a moving or a free interface.

This project aims at a simultaneous advance in a deeper understanding of outer forces and moving interfaces by investigating four circles of problems:

• effects of stochastic forcing through transport noise

• wind driven boundary condition described by a Wiener process

• strong solutions to associated free boundary problems

• fluid-structure interaction or fluid-sea-ice coupling

In contrast to the Navier-Stokes equations, the study of transport noise in the context of geophysical flows is a rather new field. The starting points are the stochastic counterparts of the classical Boussinesq and hydrostatic approximations. evolution of geophysical flows governed by the primitive equations in geometries with flat boundaries and homogeneous boundary data is rather well understood. The underlying equations are known to be strongly globally well-posed. This is no longer the case when deterministic or stochastic forces are applied or when the underlying domain is allowed to be a moving interface.

## Prinicpal investigators

Universität Kassel | karoline.disser@ mathematik.uni-kassel.de | |

Technische Universität Darmstadt | hieber@ mathematik.tu-darmstadt.de
| |

University of Cambridge | est42@ damtp.cam.ac.uk |