Fast flow asymptotics for stochastic incompressible viscous fluids in R2 and SPDEs on graphs
成果类型：
Article
署名作者：
Cerrai, Sandra; Freidlin, Mark
署名单位：
University System of Maryland; University of Maryland College Park
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-018-0839-8
发表日期：
2019
页码：
491-535
关键词：
摘要：
Fast advection asymptotics for a stochastic reaction-diffusion-advection equation are studied in this paper. To describe the asymptotics, we introduce a new class of SPDEs defined on a graph, corresponding to the stream function of the underlying incompressible flow. We prove that, as the advection term becomes faster and faster, the solution of the stochastic reaction-diffusion-advection equation on the plane converges in a suitable sense to the solution of such an SPDE defined on the graph. This result is a consequence of averaging, due to a probabilistic representation of solutions, both for the SPDEs on the plane and for the SPDE on the graph.
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