In this talk, we consider the Muskat problem, modeling the dynamics of two incompressible immiscible fluids in porous media. First, we consider fluids of different densities. This case has been extensively studied recently, in particular because its very interesting features. The fluids can be stabl...

The Landau equation introduced by Landau in the 1930's is an important partial differential equation in kinetic theory. It gives a description of colliding particles in plasma physics, and it can be formally derived as a limit of the Boltzmann equation where grazing collisions are dominant. The purp...

Lagrangian translating solitons are Lagrangian submanifolds in complex Euclidean spaces that evolve under the Lagrangian mean curvature flow (LMCF) by translations. They are examples of eternal solutions to LMCF, so they provide possible candidates of the local models of finite-time singularities of...