Analysis Seminar

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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.

Synopsis:

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.