Björn Bringmann (UCLA): Probabilistic global well-posedness for radial nonlinear wave equations

am Mittwoch, 18.07.2018 14:15 im Raum M5
Mathematik und Informatik

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.

Angelegt am Freitag, 15.06.2018 12:04 von cgiet_01
Geändert am Donnerstag, 05.07.2018 09:29 von cgiet_01
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Kolloquium der angewandten Mathematik