Speaker: Ben Harrop-Griffiths (UC Berkeley)

Title: The lifespan of small solutions to the KP-I

Abstract: We show that for small, localized initial data there exists a global solution to the KP-I equation in a Galilean-invariant space using the method of testing by wave packets. This is joint work with Mihaela Ifrim and Daniel Tataru.

Speaker: Alan Hammond (UC Berkeley)

Title: Moment bounds and mass-conservation in PDE modelling coalescence

Abstract: We examine the behaviour of solutions to a system of PDE
(the Smoluchowski PDE), that model the aggregation of
mass-bearing particles that diffuse and are prone to
coagulate in pairs at close range. Conditions under which
these solutions conserve mass for all time will be
presented, along with stronger estimates, moment bounds
that show that heavy particles are rare. Uniqueness of
solutions also follows from the moment bounds.

This is joint work with Fraydoun Rezakhanlou.

Speaker: Maciej Zworski (UC Berkeley)

Title: Stochastic stability of Ruelle resonances

Abstract: click here.

A centre-stable manifold for the energy-critical wave equation in \(\mathbb{R}^3\) in the symmetric setting.