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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2205.04642 |
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| _version_ | 1866909409396916224 |
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| author | Ahn, Jaeseop Kim, Seongyeon Seo, Ihyeok |
| author_facet | Ahn, Jaeseop Kim, Seongyeon Seo, Ihyeok |
| contents | We study the long time behaviour of solutions for the weakly damped forced Kawahara equation on the torus. More precisely, we prove the existence of a global attractor in $L^2$, to which as time passes all solutions draw closer. In fact, we show that the global attractor turns out to lie in a smoother space $H^2$ and be bounded therein. Further, we give an upper bound of the size of the attractor in $H^2$ that depends only on the damping parameter and the norm of the forcing term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_04642 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Global attractor for the weakly damped forced Kawahara equation on the torus Ahn, Jaeseop Kim, Seongyeon Seo, Ihyeok Analysis of PDEs We study the long time behaviour of solutions for the weakly damped forced Kawahara equation on the torus. More precisely, we prove the existence of a global attractor in $L^2$, to which as time passes all solutions draw closer. In fact, we show that the global attractor turns out to lie in a smoother space $H^2$ and be bounded therein. Further, we give an upper bound of the size of the attractor in $H^2$ that depends only on the damping parameter and the norm of the forcing term. |
| title | Global attractor for the weakly damped forced Kawahara equation on the torus |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2205.04642 |