三维不可压Navier-Stokes方程组轨道统计解的退化正则性

Degenerate Regularity of Trajectory Statistical Solutions for the 3D Incompressible Navier-Stokes Equations

该文研究三维自治不可压Navier-Stokes方程组轨道统计解的退化正则性.作者证明了当该方程组的外力项具有H^(-1)正则性且Grashof数小于2.057时它的弱轨道统计解退化成具有部分正则性的统计解.同时也证明了当外力项具有L^(2)正则性且Grashof数小于2.057时它的轨道统计解退化成强轨道统计解.

In this article,the authors prove that if the(generalized)3D Grashof number of the 3D autonomous incompressible Navier-Stokes equations is less than 2.057,then its weak trajectory statistical solutions possess(partial)degenerate regularity in the sense that they are supported by a set in which the weak solutions are in fact(partially)strong solutions.Also,they reveal that if the 3D Grashof number is less than 2.057,then the 3D incompressible Navier-Stokes equations possess only one complete and bounded strong solution which not only forward attracts but also pullback attracts its trajectories.