Global well-posedness of the dynamic $\Phi^{4}$ model in the plane

Jean-Christophe Mourrat; Hendrik Weber

doi:10.1214/16-AOP1116

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Home > Journals > Ann. Probab. > Volume 45 > Issue 4 > Article

July 2017 Global well-posedness of the dynamic $\Phi^{4}$ model in the plane

Jean-Christophe Mourrat, Hendrik Weber

Ann. Probab. 45(4): 2398-2476 (July 2017). DOI: 10.1214/16-AOP1116

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Abstract

We show global well-posedness of the dynamic $\Phi^{4}$ model in the plane. The model is a nonlinear stochastic PDE that can only be interpreted in a “renormalised” sense. Solutions take values in suitable weighted Besov spaces of negative regularity.

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Jean-Christophe Mourrat. Hendrik Weber. "Global well-posedness of the dynamic $\Phi^{4}$ model in the plane." Ann. Probab. 45 (4) 2398 - 2476, July 2017. https://doi.org/10.1214/16-AOP1116

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Received: 1 January 2015; Revised: 1 February 2016; Published: July 2017

First available in Project Euclid: 11 August 2017

zbMATH: 1381.60098

MathSciNet: MR3693966

Digital Object Identifier: 10.1214/16-AOP1116

Subjects:

Primary: 35K55 , 60H15 , 81T27 , 81T40

Keywords: Nonlinear stochastic PDE , Quantum field theory , stochastic quantisation equation , weighted Besov space

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Vol.45 • No. 4 • July 2017

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Jean-Christophe Mourrat, Hendrik Weber "Global well-posedness of the dynamic $\Phi^{4}$ model in the plane," The Annals of Probability, Ann. Probab. 45(4), 2398-2476, (July 2017)

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