三维不可压Navier-Stokes方程组轨道统计解的退化正则性

Abstract

Abstract:

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.

Key words: Trajectory statistical solution, Degenerate regularity, 3D incompressible Navier-Stokes equations, Trajectory attractor, Grashof number

CLC Number:

O.175.8

Mingyue Xu,Caidi Zhao,Caraballo Tomás. Degenerate Regularity of Trajectory Statistical Solutions for the 3D Incompressible Navier-Stokes Equations[J].Acta mathematica scientia,Series A, 2021, 41(2): 336-344.

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

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