[Settfa] Seminar 10.10.2023, 10:00

[Wieslaw Kubis]

Dear all,

Below is the announcement of the next seminar.

All the best,

Wieslaw


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Well-posedness of a PDE in fluid dynamics and approximation properties 
in Lipschitz-free spaces 
<https://www.math.cas.cz/index.php/events/event/3627>

Richard Smith

University College Dublin

Tuesday, 10 October 2023 - 10:00 to 11:00IM, konírna

In this talk we present results in two areas that are very distantly 
related via optimal transport theory. In the first part, we introduce 
the ``Geometric Thin-Film equation'', which is a mathematical model of 
droplet spreading in the long-wave limit, which includes a 
regularization of the contact-line singularity. We sketch a proof of the 
existence of weak solutions of this equation, and their well-posedness 
with respect to the 1-Wasserstein distance, provided the initial 
conditions (which are Radon measures on $\R$) have no atoms. This part 
is joint work with L. Ó Náraigh and K. E. Pang (UCD).


In the second part, we consider a compact metrisable space or, more 
generally, a ``properly metrisable'' topological space $T$, together 
with the set of all compatible proper metrics $\mathcal{M}^T$, equipped 
with the uniform topology. We present a sketch of the fact that if $T$ 
is uncountable then the set of metrics $d$ for which the Lipschitz-free 
space $\mathcal{F}{(T,d)}$ fails the approximation property is dense in 
$\mathcal{M}^T$. We also show that, if $T$ is compact, then the set of 
metrics $d$ for which $\mathcal{F}{(T,d)}$ has the metric approximation 
property is also dense in $\mathcal{M}^T$. This part is joint work with 
F. Talimdjioski (UCD).