“From the Heat equation to Navier-Stokes: a dynamic approach to regularity”
Giovedì 18 Novembre 2025, ore 17:00 - Aula 2AB40 - Alessandro Violini (University of Basel)
Abstract
We will study the evolution of the motion of a fluid surrounded by vacuum. This evolution is described by the two-dimensional incompressible Navier-Stokes equations. The regularity of the motion depends both on the smoothness of the initial velocity field of the fluid and on the geometry of the region $\Omega$ initially occupied by it. In particular, we are interested in the case where $\Omega$ is a Lipschitz domain. We will show that, under a mild regularity assumption on the initial velocity field (belonging to a critical Besov space), the evolved region $\Omega_t$ remains Lipschitz. The proof relies on Dynamic Interpolation, a time-dependent version of the classical Real Interpolation method for Banach spaces. To introduce this technique and the role of Besov spaces, we will first discuss the heat equation as a simpler toy model for the Navier–Stokes system.
