Presented by:
Augustin Moinat
Date:
Wednesday 7th November 2018 - 15:00 to 15:30
Venue:
INI Seminar Room 2
Abstract:
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 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 treat the
large and small scale behaviour of solutions with completely different
arguments. For small scales
we use bounds very much akin to those presented in Hairer's 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.
The fact that our
bounds do not depend on space-time boundary conditions makes them useful for the
analysis of large scale properties of solutions. They can for example
be used in a
compactness argument to construct solutions on the full space and their invariant
measures.
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