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Dissipativity of Fractional Navier–Stokes Equations with Variable Delay

Author

Listed:
  • Lin F. Liu

    (School of Mathematics, Northwest University, Xi’an 710075, China)

  • Juan J. Nieto

    (Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain)

Abstract

We use classical Galerkin approximations, the generalized Aubin–Lions Lemma as well as the Bellman–Gronwall Lemma to study the asymptotical behavior of a two-dimensional fractional Navier–Stokes equation with variable delay. By modifying the fractional Halanay inequality and the comparison principle, we investigate the dissipativity of the corresponding system, namely, we obtain the existence of global absorbing set. Besides, some available results are improved in this work. The existence of a global attracting set is still an open problem.

Suggested Citation

  • Lin F. Liu & Juan J. Nieto, 2020. "Dissipativity of Fractional Navier–Stokes Equations with Variable Delay," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2037-:d:445573
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    References listed on IDEAS

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    1. Harikrishnan, S. & Prakash, P. & Nieto, J.J., 2015. "Forced oscillation of solutions of a nonlinear fractional partial differential equation," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 14-19.
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