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# Jason Metcalfe, UNC-Chapel-Hill – Analysis & PDE Seminar

## November 17, 2021 @ 4:00 pm - 5:00 pm

Mode: In-person

TITLE: Variants of r^p weighted local energy estimates and their application to long time existence for nonlinear wave equations

ABSTRACT: We will examine long-time existence for nonlinear wave equations (1) satisfying the null condition, (2) containing dependence on the solution at the lowest order, and (3) satisfying a certain weak null condition. The method of proof relies on a space-time Klainerman Sobolev estimate and a local energy estimate that is a variant of the r^p weighted estimates. Efforts will be made to keep the talk relatively accessible to graduate students that may be interested in the field.