A note on the existence of a global attractor for the Brinkman-Forchheimer equations. (English) Zbl 1177.35039
Summary: This study focuses on the Brinkman-Forchheimer equation \(u_t=\gamma \Delta u- au- b|u|u- c|u|^\beta u- \nabla p+f\) in an open, bounded domain \(\varOmega \) and the existence of a global attractor in the phase space \(\widetilde{H}_0^1(\Omega)\) is established.
MSC:
| 35B41 | Attractors |
| 35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
| 47D06 | One-parameter semigroups and linear evolution equations |
References:
| [1] | Uǧurlu, D., On the existence of a global attractor for the Brinkman-Forchheimer equations, Nonlinear Anal., 68, 1986-1992 (2008) · Zbl 1137.35316 |
| [2] | Ma, Q.; Wang, S.; Zhong, C., Necessary and sufficient conditions for the existence of the global attractors for a nonlinear wave equations, Indiana Math. J., 5, 1542-1558 (2002) |
| [3] | Temam, R., (Infinite Dimensional Dynamical Systems in Mechanics and Physics. Infinite Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Sciences, vol. 68 (1988), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0662.35001 |
| [4] | Constantin, P.; Foias, C., Navier-Stokes Equations (1989), Univ. Chicago Press: Univ. Chicago Press Chicago, London |
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