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FENG Zhen-zhen, WU Luo. Large time behavior of a solution for the modified Navier-Stokes equations[J]. Journal of East China Normal University (Natural Sciences), 2010, (5): 56-66.
Citation:
FENG Zhen-zhen, WU Luo. Large time behavior of a solution for the modified Navier-Stokes equations[J]. Journal of East China Normal University (Natural Sciences), 2010, (5): 56-66.
FENG Zhen-zhen, WU Luo. Large time behavior of a solution for the modified Navier-Stokes equations[J]. Journal of East China Normal University (Natural Sciences), 2010, (5): 56-66.
Citation:
FENG Zhen-zhen, WU Luo. Large time behavior of a solution for the modified Navier-Stokes equations[J]. Journal of East China Normal University (Natural Sciences), 2010, (5): 56-66.
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.