Existence and Uniqueness of Stationary Solutions for 3D Navier–Stokes System with Small Random Forcing via Stochastic Cascades
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- 作者：Yuri Bakhtin
- 关键词：Navier– ; Stokes system ; Stationary solution ; Stochastic cascades ; “ ; One force– ; one solution” ; Principle
- 刊名：Journal of Statistical Physics
- 出版时间：January 2006
- 出版年：2006
- 期刊代码：19_00224715
- 类别：ph
- 卷：122
- 期：2
- 页码：351-360
- 数据来源：sp
摘要
We consider the 3D Navier–Stokes system in the Fourier space with regular forcing given by a stationary in time stochastic process satisfying a smallness condition. We explicitly construct a stationary solution of the system and prove a uniqueness theorem for this solution in the class of functions with Fourier transform majorized by a certain function h. Moreover we prove the following “one force—one solution” principle: the unique stationary solution at time t is presented as a functional of the realization of the forcing in the past up to t. Our explicit construction of the solution is based upon the stochastic cascade representation.