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Transactions of the American Mathematical Society

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Renormalization of the two-dimensional stochastic nonlinear wave equations


Authors: Massimiliano Gubinelli, Herbert Koch and Tadahiro Oh
Journal: Trans. Amer. Math. Soc. 370 (2018), 7335-7359
MSC (2010): Primary 35L71, 60H15
DOI: https://doi.org/10.1090/tran/7452
Published electronically: June 7, 2018
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Abstract: We study the two-dimensional stochastic nonlinear wave equations (SNLW) with an additive space-time white noise forcing. In particular, we introduce a time-dependent renormalization and prove that SNLW is pathwise locally well-posed. As an application of the local well-posedness argument, we also establish a weak universality result for the renormalized SNLW.


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Massimiliano Gubinelli
Affiliation: Hausdorff Center for Mathematics & Institut für Angewandte Mathematik, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany
Email: gubinelli@iam.uni-bonn.de

Herbert Koch
Affiliation: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany
Email: koch@math.uni-bonn.de

Tadahiro Oh
Affiliation: School of Mathematics, The University of Edinburgh, and The Maxwell Institute for the Mathematical Sciences, James Clerk Maxwell Building, The King’s Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
Email: hiro.oh@ed.ac.uk

DOI: https://doi.org/10.1090/tran/7452
Keywords: Stochastic nonlinear wave equation, nonlinear wave equation, renormalization, Wick ordering, Hermite polynomial, white noise
Received by editor(s): March 23, 2017
Published electronically: June 7, 2018
Additional Notes: The first author was partially supported by the DFG through CRC 1060
The second author was partially supported by the DFG through CRC 1060
The third author was supported by the ERC starting grant no. 637995 “ProbDynDispEq”
Article copyright: © Copyright 2018 American Mathematical Society

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