Zusammenfassung für den Vortrag am 12.01.2015 (11:00 Uhr)
Arbeitsgemeinschaft ANGEWANDTE ANALYSISHao Shen (University of Warwick)
Theory of regularity structures and dynamical Sine-Gordon model
We discuss the dynamical sine-Gordon equation in two space dimension with parameter β. Our main result is that when β2 < 16π∕3, the Wick renormalised equation is locally well-posed. We aim to use this particular equation as an example to illustrate the general ideas in the theory of regularity structures recently developed by Martin Hairer. A main feature of this model is that when β2 < 4π, previous solution theory applies, while for β2 ∈ [4π,16π∕3), one has to apply the theory of regularity structures. This is joint work with Martin Hairer.