OS Stochastische Analysis Detailseite Kalender

Speaker:
Prof. Dr. Nicolas Perkowski (Freie Universität Berlin)

Abstract: The Φ^4_3 equation is a singular stochastic PDE with important applications in mathematical physics. Its solution usually requires advanced mathematical theories like regularity structures or paracontrolled distributions, and even local well-posedness is highly nontrivial. I will present a multiplicative transformation which reduces the periodic Φ^4_3 equation to a well-posed random PDE. This leads to a simple and elementary proof of global well-posedness, which only relies on Schauder estimates, the maximum principle, and basic estimates for paraproducts, and in particular it does not need regularity structures or paracontrolled distributions.

This is a joint work with Aukosh Jagannath.