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Vietnam Journal of Mathematics 40:1 (2012)
57-78
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g-Navier-Stokes Equations with Infinite Delays
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Cung The Anh1 and Dao Trong
Quyet2
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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
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Received July 13, 2011
Revised October 24, 2011
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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.
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2000 Mathematics
Subject Classification. 35B41, 35Q30, 37L30, 35D05.
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Keywords. g-Navier-Stokes equations,
infinite delay, weak solution, the Galerkin method, station-ary solution, global
stability.
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Established
by Vietnam Academy of Science and Technology & Vietnam
Mathematical Society
Published by
Springer since January 2013
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