Regularization by noise and stochastic Burgers equations
Gubinelli, Massimiliano; Jara, Milton (2013), Regularization by noise and stochastic Burgers equations, Stochastic Partial Differential Equations: Analysis and Computations, 1, 2, p. 325-350. http://dx.doi.org/10.1007/s40072-013-0011-5
Type
Article accepté pour publication ou publiéExternal document link
http://arxiv.org/abs/1208.6551v2Date
2013Journal name
Stochastic Partial Differential Equations: Analysis and ComputationsVolume
1Number
2Publisher
Springer
Pages
325-350
Publication identifier
Metadata
Show full item recordAbstract (EN)
We study a generalized 1d periodic SPDE of Burgers type: ∂tu=−Aθu+∂xu2+Aθ/2ξ where θ>1/2 , −A is the 1d Laplacian, ξ is a space–time white noise and the initial condition u0 is taken to be (space) white noise. We introduce a notion of weak solution for this equation in the stationary setting. For these solutions we point out how the noise provide a regularizing effect allowing to prove existence and suitable estimates when θ>1/2 . When θ>5/4 we obtain pathwise uniqueness. We discuss the use of the same method to study different approximations of the same equation and for a model of stationary 2d stochastic Navier–Stokes evolution.Subjects / Keywords
Noise regularization; SPDEs; Kardar–Parisi–Zhang equationRelated items
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