Version 1
: Received: 30 August 2019 / Approved: 2 September 2019 / Online: 2 September 2019 (04:30:06 CEST)
Version 2
: Received: 12 February 2021 / Approved: 18 February 2021 / Online: 18 February 2021 (10:40:32 CET)
How to cite:
Zheng, Y.; Liu, W.; Liu, Y. Well-Posedness and Long-Time Behavior of Solutions for Two-Dimensional Navier-Stokes Equations with Infinite Delay and General Hereditary Memory. Preprints2019, 2019090008. https://doi.org/10.20944/preprints201909.0008.v2
Zheng, Y.; Liu, W.; Liu, Y. Well-Posedness and Long-Time Behavior of Solutions for Two-Dimensional Navier-Stokes Equations with Infinite Delay and General Hereditary Memory. Preprints 2019, 2019090008. https://doi.org/10.20944/preprints201909.0008.v2
Zheng, Y.; Liu, W.; Liu, Y. Well-Posedness and Long-Time Behavior of Solutions for Two-Dimensional Navier-Stokes Equations with Infinite Delay and General Hereditary Memory. Preprints2019, 2019090008. https://doi.org/10.20944/preprints201909.0008.v2
APA Style
Zheng, Y., Liu, W., & Liu, Y. (2021). Well-Posedness and Long-Time Behavior of Solutions for Two-Dimensional Navier-Stokes Equations with Infinite Delay and General Hereditary Memory. Preprints. https://doi.org/10.20944/preprints201909.0008.v2
Chicago/Turabian Style
Zheng, Y., Wenjun Liu and Yadong Liu. 2021 "Well-Posedness and Long-Time Behavior of Solutions for Two-Dimensional Navier-Stokes Equations with Infinite Delay and General Hereditary Memory" Preprints. https://doi.org/10.20944/preprints201909.0008.v2
Abstract
We address the dynamics of two-dimensional Navier-Stokes models with infinite delay and hereditary memory, whose kernels are a much larger class of functions than the one considered in the literature, on a bounded domain. We prove the existence and uniqueness of weak solutions by means of Faedo-Galerkin method. Moreover, we establish the existence of global attractor for the system with the existence of a bounded absorbing set and asymptotic compact property.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received:
18 February 2021
Commenter:
Wenjun Liu
Commenter's Conflict of Interests:
Author
Comment: We have changed the sentence at the end of section 2 as "In addition, we define the space $\mathcal{H}^{*}:=BCL_{-\infty}(H)\times L^{2}_{\mu}(\mathbb{R^{+}},V)$ with the following norm $$\|(\psi,\varphi)\|^{2}_{\mathcal{H}^{*}}=\|\psi\|^{2}_{BCL_{-\infty}(H)}+\|\varphi\|^{2}_{1,\mu}.$$" and other related places.
Commenter: Wenjun Liu
Commenter's Conflict of Interests: Author
$$\|(\psi,\varphi)\|^{2}_{\mathcal{H}^{*}}=\|\psi\|^{2}_{BCL_{-\infty}(H)}+\|\varphi\|^{2}_{1,\mu}.$$" and other related places.