Dissipativity of Fractional Navier–Stokes Equations with Variable Delay

Lin F. Liu and Juan J. Nieto
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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

Mathematics, 2020, vol. 8, issue 11, 1-20

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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