Oberseminar Mathematik in den Naturwissenschaften Stefano Scrobogna, Asymptotic models for the Muskat problem

The muskat or Hele-Shaw cell problem describes the motion of an incompressible fluid in a porous medium with a free interface which is transported by the fluid. In the talk we will construct some asymptotic simplified models in specific regimes in which is it possible to capture, mathematically, some dynamics which are elusive in the full model. We will thus analyse the case in which the surface tension is considered, thus proving some real-life interesting behaviours.