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June, 2020 Backward Stability and Divided Invariance of an Attractor for the Delayed Navier-Stokes Equation
Yangrong Li, Qiangheng Zhang
Taiwanese J. Math. 24(3): 575-601 (June, 2020). DOI: 10.11650/tjm/190603


We study backward stability of a pullback attractor especially for a delay equation. We introduce a new concept of a backward attractor, which is defined by a compact, pullback attracting and dividedly invariant family. We then show the equivalence between existence of a backward attractor and backward stability of the pullback attractor, and present some criteria by using the backward limit-set compactness of the system. In the application part, we consider the Navier-Stokes equation with a nonuniform Lipschitz delay term and a backward tempered force. Based on the fact that the delay does not change the backward bounds of the velocity field and external forces, we establish the backward-uniform estimates and obtain a backward attractor, which leads to backward stability of the pullback attractor. Some special cases of variable delay and distributed delay are discussed.


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Yangrong Li. Qiangheng Zhang. "Backward Stability and Divided Invariance of an Attractor for the Delayed Navier-Stokes Equation." Taiwanese J. Math. 24 (3) 575 - 601, June, 2020.


Received: 26 March 2019; Revised: 4 June 2019; Accepted: 17 June 2019; Published: June, 2020
First available in Project Euclid: 19 May 2020

zbMATH: 07251188
MathSciNet: MR4100710
Digital Object Identifier: 10.11650/tjm/190603

Primary: 35B41, 37L30

Rights: Copyright © 2020 The Mathematical Society of the Republic of China


Vol.24 • No. 3 • June, 2020
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