Electron. J. Differential Equations, Vol. 2017 (2017), No. 244, pp. 1-11.

Time-periodic strong solutions of the 3D Navier-Stokes equations with damping

Yongho Kim, Kwangok Li

Abstract:
This article concerns the incompressible Navier-Stokes equations with damping and homogeneous Dirichlet boundary conditions in 3D bounded domains. We find conditions on parameters to guarantee that the problem has a strong time-periodic solution and that the weak solutions of the problem converge to a unique time-periodic solution as $t\to \infty$.

Submitted May 16, 2017. Published October 5, 2017.
Math Subject Classifications: 35Q30, 76D05.
Key Words: 3D Navier-Stokes equation; asymptotic behavior; nonlinear damping; time-periodic solution.

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Yongho Kim
Department of Mathematics
University of Science
Pyongyang, DPR Korea
email: kyho555@star-co.net.kp
Kwangok Li
Department of Mathematics
University of Science
Pyongyang, DPR Korea
email: liko@star-co.net.kp

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