PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES

被引：329

作者：

Gubinelli, Massimiliano ^{[1
,2
,3
]}

Imkeller, Peter ^{[4
]}

Perkowski, Nicolas ^{[1
,2
]}

机构：

[1] Univ Paris 09, CEREMADE, F-75775 Paris 16, France

[2] Univ Paris 09, CNRS, UMR 7534, F-75775 Paris 16, France

[3] Inst Univ France, Paris, France

[4] Humboldt Univ, Inst Math, Berlin, Germany

来源：

FORUM OF MATHEMATICS PI | 2015年 / 3卷

关键词：

D O I：

10.1017/fmp.2015.2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough paths. We illustrate its applicability on some model problems such as differential equations driven by fractional Brownian motion, a fractional Burgers-type stochastic PDE (SPDE) driven by space-time white noise, and a nonlinear version of the parabolic Anderson model with a white noise potential.

引用

页数：75

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