Journal of Guangxi Normal University(Natural Science Edition) ›› 2020, Vol. 38 ›› Issue (1): 41-46.doi: 10.16088/j.issn.1001-6600.2020.01.005

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Backward-compact Dynamics for Non-autonomous Navier-Stokes Equations on Unbounded Domains

SHE Lianbing*, GAO Yunlong   

  1. School of Mathematics and Information Engineering, Liupanshui Normal College,Liupanshui Guizhou 553004, China
  • Received:2018-10-26 Online:2020-01-25 Published:2020-01-15

Abstract: This paper is devoted to the backward-compact dynamics for a non-autonomous Navier-Stokes equation. Assume that the time-dependent force is weakly backward-tempered, then we can show that the system has an increasing and bounded pullback absorbing set in an energy space. In order to overcome the loss of compact Sobolev embedding, Ball’s method of energy equation is used to show the backward asymptotical compactness of the system. Finally, it is proved that the non-autonomous Navier-Stokes equation has a backward-compact pullback attractor in the energy space.

Key words: non-autonomous Navier-Stokes equation, backward-compact dynamics, pullback attractor, energy equation, unbounded domains

CLC Number: 

  • O117.8
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