Dissipativity of Fractional Navier–Stokes Equations with Variable Delay

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URI: http://hdl.handle.net/10347/24036
E-ISSN: 2227-7390
DOI: 10.3390/math8112037

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2020

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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

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Fractional Navier–Stokes equations| Variable delay| Modified fractional Halanay inequality| Generalized comparison principle| Dissipativity

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Liu, L.F.; Nieto, J.J. Dissipativity of Fractional Navier–Stokes Equations with Variable Delay. Mathematics 2020, 8, 2037

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The work of Lin F. Liu has been partially supported by NSF of China (Nos. 11901448, 11871022 and 11671142) as well as by China Postdoctoral Science Foundation Grant (Nos. 2018M643610). The work of Juan J. Nieto has been partially supported by the Agencia Estatal de Investigación (AEI) of Spain, co-financed by the European Fund for Regional Development (FEDER) corresponding to the 2014-2020 multiyear financial framework, project MTM2016-75140-P, Xunta de Galicia under grant ED431C 2019/02; by Instituto de Salud Carlos III (Spain), grant COV20/00617

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© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)
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