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

First available in Project Euclid: 24 June 2019

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

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


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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