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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Local bounds for the dynamic $\Phi^4_3$ model
Local bounds for the dynamic $\Phi^4_3$ modelAdd to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact INI IT. This talk has been canceled/deleted 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. This talk is part of the Isaac Newton Institute Seminar Series series. This talk is included in these lists:This talk is not included in any other list Note that ex-directory lists are not shown. |
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