Trajectory statistical solutions for the 3D Navier–Stokes equations: The trajectory attractor approach. (June 2020)

• Record Type: Journal Article
• Authors: Zhao, Caidi; Li, Yanjiao; Song, Zhongchun
• Is Part Of: Nonlinear analysis. Volume 53(2020)
• Publication Date: 2020-06
• Subjects: 3D Navier–Stokes equations -- Trajectory statistical solution -- Trajectory attractor; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.103077
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this article, we construct the trajectory statistical solution for the 3D incompressible Navier–Stokes equations via the natural translation semigroup and trajectory attractor. In our construction, the trajectory statistical solution is an invariant space–time probability measure which is carried by the trajectory attractor of the natural translation semigroup defined on the trajectory space, and the trajectory statistical solution possesses the invariant property under the acting of the translation semigroup.