Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Advance publication (2019), 27 pages.
Backward Stability and Divided Invariance of an Attractor for the Delayed Navier-Stokes Equation
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.
Taiwanese J. Math., Advance publication (2019), 27 pages.
First available in Project Euclid: 24 June 2019
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Digital Object Identifier
Primary: 35B41: Attractors 37L30: Attractors and their dimensions, Lyapunov exponents
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