Analysis Seminar 2020/21

The Analysis and Differential Equations Seminar takes place on Thursdays at 2.15 via zoom in even weeks.
If you have any queries, or if you would like to be on our e-mail list, please contact the organisers Karsten Matthies and Monica Musso.

Autumn 2020

Date Speaker Title/Abstract
8 Oct Shrish Parmeshwar
University of Bath
Global-in-Time Solutions to the N-Body Euler-Poisson System
We investigate the N-Body compressible Euler-Poisson system, modelling multiple stars interacting with each other via Newtonian gravity. If we prescribe initial data so that each star expands indefinitely, one might expect that two of them will collide in finite time due to their expansion, and the influence of gravity. In this talk we show that there exists a large family of initial positions and velocities for the system such that each star can expand for all time, but no two will touch in finite time. To do this we use a scaling mechanism present in the compressible Euler system, and a careful analysis of how the gravitational interaction between stars affects their dynamics.
22 Oct Jarrod Williams
University of Bath
Elliptic structures in the Gauss-Codazzi-Mainardi equations, with applications to General Relativity
Motivated by the problem of constructing “initial data” for the Cauchy problem in General Relativity, we discuss a certain mixed-order elliptic reduction of the Gauss-Codazzi-Mainardi (G-C-M) equations for an embedded Riemannian 3-manifold. Using this formulation, one can hope to construct perturbative solutions of the G-C-M equations for which particular components of the ambient Weyl curvature are prescribed at the outset. We show that this can be done by a simple Implicit Function Theorem argument when the background belongs to a certain family of closed hyperbolic manifolds. Moreover, the space of solutions in this case is shown to admit an explicit parametrisation via an elliptic complex.
5 Nov Antonio J. Fernández
University of Bath
Non-homogeneous Gagliardo-Nirenberg-type inequalities and a biharmonic NLS
The aim of this talk is twofold. On one hand, we investigate some non-homogeneous Gagliardo-Nirenberg-type inequalities. Special attention will be paid to the method used to prove such estimates. On the other hand, we analyse the standing waves for a fourth-order Schrödinger equation with mixed dispersion that minimize the associated energy the L2-norm (the mass) is kept fixed. The talk is based on a joint work with Louis Jeanjean, Rainer Mandel and Mihai Mariş
19 Nov Miles Wheeler
University of Bath
Existence and non-existence of solitary water waves
3 Dec No seminar


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