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Bull. Korean Math. Soc. 2018; 55(2): 379-403

Online first article January 9, 2018      Printed March 30, 2018

https://doi.org/10.4134/BKMS.b170044

Copyright © The Korean Mathematical Society.

Existence and long-time behavior of solutions to Navier-Stokes-Voigt equations with infinite delay

Cung The Anh, Dang Thi Phuong Thanh

Hanoi National University of Education, Hung Vuong University

Abstract

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In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.

Keywords: Navier-Stokes-Voigt equations, infinite delay, weak solution, Galerkin method, energy method, global attractor, stationary solution, existence, stability

MSC numbers: 76A10, 35D30, 35B35, 35Q35

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