Abstract for the talk on 21.02.2019 (15:00 h)Arbeitsgemeinschaft ANGEWANDTE ANALYSIS
Augustin Moinat (University of Warwick)
Space-time localisation for the dynamic Φ34 model
21.02.2019, 15:00 h, MPI für Mathematik in den Naturwissenschaften Leipzig, A3 01 (Sophus-Lie-SR)
We give an a priori bound for solutions of the dynamic Φ34 equation. This bound provides a control on solutions on a compact space-time set only in terms of the realisation of the noise on an enlargement of this set, and it does not depend on any choice of space-time boundary conditions. We will show the diﬀerent techniques used for the small and large scale bounds. For small scales we use techniques derived from Hairers theory of regularity structures.. For large scales we use a PDE argument based on the maximum principle. Both regimes are connected by a solution-dependent regularisation procedure.