Preprint Article Version 1 This version is not peer-reviewed

Well-Posedness and Long-Time Behavior of Solutions for Two-Dimensional Navier-Stokes Equations with Infinite Delay and General Hereditary Memory

Version 1 : Received: 30 August 2019 / Approved: 2 September 2019 / Online: 2 September 2019 (04:30:06 CEST)

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. Preprints 2019, 2019090008 (doi: 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 (doi: 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.

Subject Areas

Navier-Stokes equation; infinite delay; memory kernels

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