Loading Events

« All Events

  • This event has passed.

Global weak solutions of 3+1 dimensional vacuum Einstein equations 

April 12, 2024 @ 12:00 pm - 1:00 pm

Event Series Event Series (See All)

CMSA Member Seminar

Speaker: Puskar Mondal

Title: Global weak solutions of 3+1 dimensional vacuum Einstein equations

Abstract: It is important to understand if the `solutions’ of non-linear evolutionary PDEs persist for all time or become extinct in finite time through the blow-up of invariant entities. Now the question of this global existence or finite time blow up in the PDE settings is well defined if the regularity of the solution is specified. Most physically interesting scenarios demand control of the point-wise behavior of the solution. Unfortunately, most times this level of regularity is notoriously difficult to obtain for non-linear equations. In this talk, I will discuss very low regularity solutions namely distributional (or weak) solutions of vacuum Einsten’s equations in 3+1 dimensions. I prove that on a globally hyperbolic spacetime foliated by closed connected oriented negative Yamabe slices, weak solutions of the Einstein equations exist for all time. The monotonicity of a Coercive Entity called reduced Hamiltonian that controls the minimum regularity required for the weak solution is employed. This is in the same spirit as Leray’s global weak solutions of Navier-Stokes in 3+1 dimensions and the first result in the context of Einstein equations.


April 12, 2024
12:00 pm - 1:00 pm
Event Category:


Benjamin McKenna
Iacopo Brivio
Tomer Ezra


CMSA Room G10
CMSA, 20 Garden Street
Cambridge, MA 02138 United States
+ Google Map