Global existence and Singularities in geophysical flows

• Applicant: Dr. Tim Binz
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 538212014

The present research proposal consists of two projects: 1. splash singularities of the Hele-Shaw problem with surface tension 2. shock waves in the Stokes-Transport system with rotation. The Hele-Shaw model describes the behaviour of two immiscible fluids confined by two horizontal parallel plates which are close together. More pecisely, it describes the evolution of the interface. In the present project we consider the question whether so called "splash singularities" may occur or not. Splash singularities are points, where the interface collides with itself. Here particular attention is paid to the role of surface tension. The Stokes-transport system with rotation describes that heavy fluids sink in a rotating frame. In the present project we are interested in the behaviour of shock waves in this system. Shock waves are rough solutions that change abruptly at the wave front. In particular, we aim for existence and uniqueness of shocks, and plan to study their evolution in time.

• DFG Programme: WBP Fellowship
• International Connection: USA
• Host: Professor Dr. Peter Constantin, Ph.D.