Recent results on 2D density patches for inhomogeneous Navier-Stokes

Analysis of Fluids and Related Topics: Francisco Gancedo, Universidad de Sevilla
Mar 9 2017 - 4:30pm
Event type: 
Analysis of Fluids and Related Topics
Fine Hall 322

This talk is about the dynamics of a patch given by two fluids of different constant densities, evolving by the inhomogeneous Navier-Stokes equations. The main question to address is whether the regularity of the boundary of the initial patch is preserved in time. Using classical Sobolev spaces for the velocity, we establish the propagation of C1+γW2,∞anC^{2+\gamma}regularitiewith0<\gamma<1$. The results are based on new cancelations found for time dependent singular integrals given by the linear nonhomogeneous heat kernel acting on quadratic terms.