Non-linear waves and time-periodicity

Abstract: I will give an overview talk concerning the possible existence and stability of solutions to non-linear wave equations which are periodic in time. Such solutions can arise in a variety of mathematical models, from fluid dynamics, elasticity, and general relativity, where in particular, there were investigated numerically by Maliborski and Rostworowski (2013) for the Einstein-scalar-field model in spherically symmetry near the Anti-de-Sitter spacetime.

I will start the presentation with some reminder concerning the linear wave equation on Anti-de-Sitter before presenting some results and methods for semi-linear wave equations. In a second part, I will describe a recent construction of special coordinates for 1+1 Lorentzian metric on \mathbb{R}\times\mathcal{S}^1 with time-periodic coefficients, which is expected to be an essential step to extend the previous results to quasi linear wave equations.

This a joint work with Athanasios Chatzikaleas (National and Kapodistrian University of Athens ).

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

JoMaReC - Joint Online Mathematical Relativity Colloquium

Series comments: This monthly online colloquium is meant to be accessible to and informative for mathematicians and mathematical physicists with a background in General Relativity, widely interpreted to include Lorentzian Geometry, and Geometric Analysis of various Partial Differential Equations related to General Relativity.

It is aimed to present motivation and applications of particular results and/or introduce specific subfields, while refraining from too much technicalities.