*Article* **Dissipativity of Fractional Navier–Stokes Equations with Variable Delay**

#### **Lin F. Liu 1 and Juan J. Nieto 2,\***


Received: 14 October 2020; Accepted: 9 November 2020; Published: 16 November 2020

**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.

**Keywords:** fractional Navier–Stokes equations; variable delay; modified fractional Halanay inequality; generalized comparison principle; dissipativity
