The $H^1$-uniform attractor for the 2D non-autonomous tropical climate model on some unbounded domains
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In this paper, we study the uniform attractor of the 2D non-autonomous tropical climate model in an arbitrary unbounded domain on which the Poincar\'e inequality holds. We prove that the uniform attractor is compact not only in the $L^2$-spaces but also in the $H^1$-spaces. Our proof is based on the concept of asymptotical compactness. Finally, for the quasiperiodical external force case, the dimension estimates of such a uniform attractor are also obtained.
Abstract
In this paper, we study the uniform attractor of the 2D non-autonomous tropical climate model in an arbitrary unbounded domain on which the Poincar\'e inequality holds. We prove that the uniform attractor is compact not only in the $L^2$-spaces but also in the $H^1$-spaces. Our proof is based on the concept of asymptotical compactness. Finally, for the quasiperiodical external force case, the dimension estimates of such a uniform attractor are also obtained.
참고문헌 (36)
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