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SUMMARY:Space-time localisation for the dynamic $\\Phi^4_3$ model - Hendri
 k Weber (University of Bath)
DTSTART:20181213T090000Z
DTEND:20181213T100000Z
UID:TALK115747@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We prove an a priori bound for solutions of the dynamic $Phi^4
 _3$ equation. This bound provides a control on solutions on a compact spac
 e-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 treat the large and small scale behaviour of solutions wi
 th completely different arguments.  For small scales we use bounds akin to
  those presented in Hairer&#39\;s theory of regularity structures. For lar
 ge scales we use a PDE argument based on the maximum principle. Both regim
 es are connected by a solution-dependent regularisation procedure.  The fa
 ct that our bounds do not depend on space-time boundary conditions makes t
 hem useful for the analysis of large scale properties of solutions. They c
 an for example be used in a compactness argument to construct solutions on
  the full space and their invariant measures.  Joint work with A. Moinat.
LOCATION:Seminar Room 1\, Newton Institute
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