Björn Bringmann (UCLA): Probabilistic global well-posedness
for radial nonlinear wave equations
am Mittwoch, 18.07.2018 14:15 im Raum M5
In this talk we discuss the well-posedness of nonlinear wave equations with
rough and random initial data. Even if the initial data lives at a regularity
for which deterministic ill-posedness is known, we show that one can still
construct solutions in an almost sure sense.
In the beginning of the talk we will review the basic deterministic theory
for nonlinear wave equations. Then, we will describe the construction of
the randomized initial data. The focus in this talk lies on a randomization
that yields spherically symmetric initial data. This leads to an interesting
trade-off between geometric structure (spherical symmetry) and randomness.
Finally, we will discuss the global behaviour of solutions to the radial energycritical
nonlinear wave equation with random initial data. To this end, we
introduce a novel interaction flux estimate.