Well-posedness for Nonlinear Wave Equations with Deterministic and Randomized Initial Data
A collection of notes to aid preparation for an oral
qualifying exam, a part of
the mathematics Ph.D program at UMass Amherst.
took place in the Fall of 2019.
Discusses some (mainly local) well-posedness results for
power type nonlinear wave equations in 3 spatial dimensions,
emphasizing the role of Strichartz estimates in these
results. An exposition of the 2014 paper of Professors
in which they show an IR^3 NLW Cauchy problem
with randomized initial data is well-posed
in a portion of the supercritical
regularity regime follows.