Multiscale analysis for SPDEs with quadratic nonlinearities

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Title: Multiscale analysis for SPDEs with quadratic nonlinearities
Authors: Pavliotis, G
Blomker, D
Hairer, M
Item Type: Working Paper
Abstract: In this article we derive rigorously amplitude equations for stochastic PDEs with quadratic nonlinearities, under the assumption that the noise acts only on the stable modes and for an appropriate scaling between the distance from bifurcation and the strength of the noise. We show that, due to the presence of two distinct timescales in our system, the noise (which acts only on the fast modes) gets transmitted to the slow modes and, as a result, the amplitude equation contains both additive and multiplicative noise. As an application we study the case of the one dimensional Burgers equation forced by additive noise in the orthogonal subspace to its dominant modes. The theory developed in the present article thus allows to explain theoretically some recent numerical observations from [Rob03].
Issue Date: 17-Nov-2006
Publisher: arXiv
Copyright Statement: © 2006 The Author(s).
Keywords: math.PR
60H15; 60H10
Publication Status: Published
Appears in Collections:Pure Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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