Richard Smith

will speak on

Well-posedness of the Geometric Thin-Film Equation

Time: 3:00PM
Date: Tue 24th October 2023
Location: E0.32 (beside Pi restaurant) [map]

Further information

Abstract: The Geometric Thin-Film equation is a mathematical model of droplet spreading in the long-wave limit, which includes a regularization of the contact-line singularity. In a previous talk we showed that this equation has unique solutions that are $\frac{1}{2}$-H\'older continuous for all time $t \in \mathbb{R}^+$, and which can be expressed in terms of push-forwards of the initial positive Radon data $\mu \in \mathcal{M}(\mathbb{R})^+$.

In this talk we consider well-posedness of these solutions with respect to the $1$-Wasserstein (or Kantorovich-Rubinstein) distance on the set of Radon probability measures $\mathcal{P}_1(\mathbb{R})$ having finite first moment. We show that the above solutions can be ill-posed if the initial data contains atoms, but are well-posed when the initial data is atomless. Optimal transport theory plays a key role in the proof of the second result.

This is joint work with Lennon \'O N\'araigh and Khang Ee Pang (UCD).

https://ucd-ie.zoom.us/j/67136645187

(This talk is part of the Analysis series.)

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