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<p>This paper is devoted to the long-term behavior of Navier–Stokes equations with non-autonomous distribution delay. First, we use the spectrum decomposition skill to overcome the lack of the smooth property of weak solutions, and then obtain the asymptotic compactness of the solution operators in the regular space as well as the existence, uniqueness and backward compactness of regular pullback attractors. Second, we prove the the pointwise upper semicontinuity of regular pullback attractors as the delay time tends to zero. Finally, we consider the asymptotically autonomous stability of regular pullback attractors when the time parameter goes to negative infinity. To the best of our knowledge, this is the first time to consider the regular dynamics for the Navier–Stokes equations with non-autonomous distribution delay.</p>

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Regularity and Stability of Pullback Attractors for Navier–Stokes Equations with Non-autonomous Distributed Delay

  • 期刊论文

  • 发表日期：

    2026年2月7日

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  • Qiangheng Zhang,
  • Tomás Caraballo,
  • Shuang Yang

摘要

This paper is devoted to the long-term behavior of Navier–Stokes equations with non-autonomous distribution delay. First, we use the spectrum decomposition skill to overcome the lack of the smooth property of weak solutions, and then obtain the asymptotic compactness of the solution operators in the regular space as well as the existence, uniqueness and backward compactness of regular pullback attractors. Second, we prove the the pointwise upper semicontinuity of regular pullback attractors as the delay time tends to zero. Finally, we consider the asymptotically autonomous stability of regular pullback attractors when the time parameter goes to negative infinity. To the best of our knowledge, this is the first time to consider the regular dynamics for the Navier–Stokes equations with non-autonomous distribution delay.