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.v1
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.v1
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.v1
APA Style
Zheng, Y., Liu, W., & Liu, Y. (2019). 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.v1
Chicago/Turabian Style
Zheng, Y., Wenjun Liu and Yadong Liu. 2019 "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.v1
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, Applied Mathematics
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.