On singularity formation in a Hele-Shaw model
Speaker: Hyu Nguyen, Princeton University
Location: Warren Weaver Hall 1302
Date: Thursday, November 2, 2017, 11 a.m.
I will discuss a lubrication approximation model of the interface between two immiscible fluids in a Hele-Shaw cell, derived in [Constantin et al, Physical Review E, 1993] and widely studied since. The model consists of a single one dimensional fourth-order nonlinear degenerate parabolic equation for the thickness of a thin neck of fluid, and two boundary conditions fixing the neck height and pressure jump. The issue of singularity formation will be addressed. This is joint work with P. Constantin, T. Elgindi and V. Vicol.