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Long time behavior of solutions to the damped forced generalized Ostrovsky equation below the energy space.
- Source :
-
Proceedings of the American Mathematical Society . Apr2021, Vol. 149 Issue 4, p1527-1542. 16p. - Publication Year :
- 2021
-
Abstract
- In this paper, we investigate the long time behavior of the damped forced generalized Ostrovsky equation below the energy space. First, by using Fourier restriction norm method and Tao's [k,Z]-multiplier method, we establish the multi-linear estimates, including the bilinear and trilinear estimates on the Bourgain space Xs,b. Then, combining the multi-linear estimates with the contraction mapping principle as well as L2 energy method, we establish the global well-posedness and existence of the bounded absorbing sets in L2. Finally, we show the existence of global attractor in L2 and its compactness in H5 by means of the high-low frequency decomposition method, cut-off function, tail estimate together with Kuratowski α-measure in order to overcome the non-compactness of the classical Sobolev embedding. This result improves earlier ones in the literatures, such as Goubet and Rosa [J. Differential Equations 185 (2002), no. 1, 25-53], Moise and Rosa [Adv. Differential Equations 2 (1997), no. 2, 251-296], Wang et al. [J. Math. Anal. Appl. 390 (2012), no. 1, 136-150], Wang [Discrete Contin. Dyn. Syst. 35 (2015), no. 8, 3799-3825], and Guo and Huo [J. Math. Anal. App. 329 (2007), no. 1, 392-407]. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 149
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 149775714
- Full Text :
- https://doi.org/10.1090/proc/15322