In this work we extend the paradifferential approach to quasilinear wave equations of Bahouri and Chemin to study quasilinear wave equations with distributional forcing. To achieve this, we combine their methods with the paracontrolled calculus of Gubinelli, Imkeller, and Perkowski. In two dimensions, we prove a well-posedness result for forcing with Hölder regularity better than -1/8 for an arbitrary initial data and for forcing with regularity better than -1 with restrictive initial data. This is a joint work with Nicolas Perkowski and Immanuel Zachhuber.
Period
17 Jun 2024 → 21 Jun 2024
Event title
New developments and challenges in Stochastic Partial Differential Equations