Speaker
Description
I will discuss the initial and boundary value problem for the Cahn--Hilliard equation with non-degenerate mobility and singular potential, showing that any weak solution converges to a single equilibrium under minimal assumptions, i.e., the existence of a global weak solution satisfying an energy inequality. This result also holds in the three-dimensional case, which was an open problem so far due to the lack of regularity of solutions, especially when the mobility is just a continuous function. I will then explain the rich variety of applications of this novel approach, ranging from Cahn—Hilliard-Navier--Stokes type systems with singular potential and nondegenerate mobility, to the conserved Allen—Cahn equation and even to the nonlocal Cahn—Hilliard equation in three dimensions.