Taiwanese Journal of Mathematics

Backward Stability and Divided Invariance of an Attractor for the Delayed Navier-Stokes Equation

Yangrong Li and Qiangheng Zhang

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Abstract

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.

Article information

Source
Taiwanese J. Math., Advance publication (2019), 27 pages.

Dates
First available in Project Euclid: 24 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1561341624

Digital Object Identifier
doi:10.11650/tjm/190603

Subjects
Primary: 35B41: Attractors 37L30: Attractors and their dimensions, Lyapunov exponents

Keywords
delay Navier-Stokes equation pullback attractor backward attractor divided invariance backward stability

Citation

Li, Yangrong; Zhang, Qiangheng. Backward Stability and Divided Invariance of an Attractor for the Delayed Navier-Stokes Equation. Taiwanese J. Math., advance publication, 24 June 2019. doi:10.11650/tjm/190603. https://projecteuclid.org/euclid.twjm/1561341624


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