Home

 

Recent Issues

Volume 52

1

 

 

 

Volume 51

1

2

3

4

Volume 50

1

2

3

4

Volume 49

1

2

3

4

Volume 48

1

2

3

4

Past Issues

 

The Journal

Cover

Aims and Scope

Subscription Information

Editorial Board

Instructions for Author

Contact Us

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Vietnam Journal of Mathematics 40:1 (2012) 57-78

 

g-Navier-Stokes Equations with Infinite Delays

Cung The Anh1 and Dao Trong Quyet2

1Department of Mathematics, Hanoi National University of Education,

136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

2Faculty of Information Technology, Le Quy Don Technical University,

100 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

Received July 13, 2011

Revised October 24, 2011

Abstract. We study the first initial boundary value problem for the two-dimensional non-autonomous g-Navier-Stokes equations containing infinite delay terms in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence and uniqueness of a weak solution to the problem is proved by using the Galerkin method. Moreover, we also analyze the stationary problem and, under suitable additional conditions, we obtain global exponential decay of the solution of the evolutionaryproblem to the stationary solution.

2000 Mathematics Subject Classification. 35B41, 35Q30, 37L30, 35D05.

Keywords. g-Navier-Stokes equations, infinite delay, weak solution, the Galerkin method,  station-ary solution, global stability.

 

 

 

Established by Vietnam Academy of Science and Technology & Vietnam Mathematical Society
Published by Springer since January 2013