Global-in-time regularity of the two-dimensional incompressible Navier-Stokes equations with variable viscosity coefficient

by Prof. Xian Liao (KIT, Karlsruhe)

Thursday Jan 30, 2025, 2:15 PM → 4:00 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

In this talk, we investigate the global-in-time regularity of the two-dimensional incompressible Navier-Stokes equations in the presence of large variations in the viscosity coefficient. Through the analysis of two good unknowns, which are associated to the viscous stress tensor globally resp. locally, we establish the Lipschitz continuity of the velocity field, even when its normal derivative exhibits discontinuities across viscosity-interfaces. Specifically, we demonstrate that the two-phase two-dimensional Navier-Stokes equations admit a unique global-in-time solution that maintains the regularity of the free interface. This is joint work with Rebekka Zimmermann (KIT).