Trajectory statistical solutions for the 3D Navier–Stokes equations: The trajectory attractor approach

Publication date: June 2020Source: Nonlinear Analysis: Real World Applications, Volume 53Author(s): Caidi Zhao, Yanjiao Li, Zhongchun SongAbstractIn 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.

Source: Nonlinear Analysis: Real World Applications - December 27, 2019 Category: Research Source Type: research