Dissipativity of Fractional Navier–Stokes Equations with Variable Delay
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...
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MDPI AG
2020-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/2037 |
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doaj-1f20fce5383e4b45b4757792399d29942020-11-25T04:11:11ZengMDPI AGMathematics2227-73902020-11-0182037203710.3390/math8112037Dissipativity of Fractional Navier–Stokes Equations with Variable DelayLin F. Liu0Juan J. Nieto1School of Mathematics, Northwest University, Xi’an 710075, ChinaInstituto de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, SpainWe 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.https://www.mdpi.com/2227-7390/8/11/2037fractional Navier–Stokes equationsvariable delaymodified fractional Halanay inequalitygeneralized comparison principledissipativity |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Lin F. Liu Juan J. Nieto |
| spellingShingle |
Lin F. Liu Juan J. Nieto Dissipativity of Fractional Navier–Stokes Equations with Variable Delay Mathematics fractional Navier–Stokes equations variable delay modified fractional Halanay inequality generalized comparison principle dissipativity |
| author_facet |
Lin F. Liu Juan J. Nieto |
| author_sort |
Lin F. Liu |
| title |
Dissipativity of Fractional Navier–Stokes Equations with Variable Delay |
| title_short |
Dissipativity of Fractional Navier–Stokes Equations with Variable Delay |
| title_full |
Dissipativity of Fractional Navier–Stokes Equations with Variable Delay |
| title_fullStr |
Dissipativity of Fractional Navier–Stokes Equations with Variable Delay |
| title_full_unstemmed |
Dissipativity of Fractional Navier–Stokes Equations with Variable Delay |
| title_sort |
dissipativity of fractional navier–stokes equations with variable delay |
| publisher |
MDPI AG |
| series |
Mathematics |
| issn |
2227-7390 |
| publishDate |
2020-11-01 |
| description |
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. |
| topic |
fractional Navier–Stokes equations variable delay modified fractional Halanay inequality generalized comparison principle dissipativity |
| url |
https://www.mdpi.com/2227-7390/8/11/2037 |
| work_keys_str_mv |
AT linfliu dissipativityoffractionalnavierstokesequationswithvariabledelay AT juanjnieto dissipativityoffractionalnavierstokesequationswithvariabledelay |
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