Patch Evolution in 2D Inhomogeneous Navier–Stokes.

Author : Paula Luna Velasco

Title : Patch Evolution in 2D Inhomogeneous Navier–Stokes

Location : Seminario 1, IMAG

Organizer : Seminario de Jóvenes Investigadores

Abstract : The motion of incompressible fluids is described by the Navier–Stokes equations, a fundamental model in mathematical physics. In two dimensions, these equations are globally well-posed for regular initial data, in contrast with the open problem in 3D. In this talk, I will focus on the inhomogeneous two-fluid system, where the fluid regions have different nonnegative densities and may exhibit a small jump in viscosity. Our main interest lies in the well-posedness of the system and in understanding the evolution and regularity of the patch boundary. I will present recent results and techniques that address the key analytical challenges of this problem. This is a joint work with Francisco Gancedo and Eduardo García-Juárez.