Large time behavior of a solution for the modified Navier-Stokes equations
Feng Zhenzhen, Wu Sheng Luo · Huadong Shifan Daxue xuebao. Ziran kexue ban · 2010
In 1966,O.A.Ladyzhenskaya proposed a kind of modified Navier-Stokes equations to describe the three-dimensional nonstationary flows of viscous incompressible fluids without assuming small gradients of the velocities.This paper considered large time behavior of a solution for the modified Navier-Stokes equations in a bounded domain and showed that decay of the solution is exactly of exponential type when force term is equal to zero.Moreover the ratio of the enstrophy over the energy has a limit as time tends to infinity,and the limit is an eigenvalue of the Stokes operator.