发表机构
University of York; Chongqing University（约克大学; 重庆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将三维随机Navier-Stokes方程的结果从有界域推广到有界与无界域，通过局部解加Lyapunov函数方法，证明了对任意$H^1$初始数据全局解的存在唯一性，并利用强噪声防止爆破。
AI 中文摘要
本工作的目标是将Hong、Li和Liu近期论文中的结果从有界域扩展到有界域和无界域。我们证明了具有非线性乘性噪声的三维随机Navier-Stokes方程对于Sobolev空间$H^1$中的每一个初始数据都存在全局解且唯一。我们不使用任何紧性论证。相反，我们首先证明局部极大解的存在性，然后利用Lyapunov函数证明解是全局的。我们的方法受到第一作者与Ferrario、Maurelli和Zanella近期关于随机非线性Schrödinger方程类似结果的论文的启发。主要思想是，一旦建立了强解的局部存在性，一个非常强的、将解推向原点的噪声将使爆破变得不可能。
英文摘要
The aim of this work is to extend the results from a recent paper by Hong, Li and Liu, from bounded domains to both bounded and unbounded domains. We show the global existence and uniqueness of 3D stochastic Navier-Stokes equations with nonlinear multiplicative noise for every initial data from the Sobolev space $H^1$. We do not use any tightness argument. Instead, we firstly show the existence of a local maximal solution and then we use Lyapunov function to prove the solution is global. Our approach is motivated by a recent paper of the first named author with Ferrario, Maurelli and Zanella about a similar result for stochastic nonlinear Schrödinger Equations. The main idea is that once the local existence of strong solutions is established, a very strong noise pushing toward the origin, will make blow-up impossible.
Comments65 pages
