Jungkyoung Na will give a talk on 04/15/2025.

In this talk, we will discuss the result I obtained last year regarding the existence of global self-similar solutions to the 3D Muskat equation. The Muskat problem is a classic free boundary problem in fluid dynamics, which models the evolution of the interface between distinct immiscible and incompressible fluids (such as water and oil, or saltwater and freshwater) as they move through porous media like sand. Additionally, we will explore the differences between our self-similar solutions and solutions of the linearized equation around the flat interface, particularly in terms of critical Sobolev spaces.