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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.16441 |
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| _version_ | 1866911522430648320 |
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| author | Cardoso, Mykael Santos, Gleison do N. de Moura, Roger P. |
| author_facet | Cardoso, Mykael Santos, Gleison do N. de Moura, Roger P. |
| contents | In this paper we establish exponential decay results for solutions of the damped $n$-dimensional Zakharov--Kuznetsov equation for $2 \le n \le 3$. More precisely, we prove the exponential decay of the $L^2(\mathbb{R}^n)$ norm when the damping is localized. In addition, when the dissipative mechanism acts on the whole space $\mathbb{R}^n$, we prove the exponential decay of the $H^1(\mathbb{R}^n)$ norm. Our strategy of proof combines a Kato's type smoothing effect, unique continuation and an observability inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16441 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the stabilization of $L^2$ and $H^1$ norms for the Zakharov-Kuznetsov equation with damping Cardoso, Mykael Santos, Gleison do N. de Moura, Roger P. Analysis of PDEs In this paper we establish exponential decay results for solutions of the damped $n$-dimensional Zakharov--Kuznetsov equation for $2 \le n \le 3$. More precisely, we prove the exponential decay of the $L^2(\mathbb{R}^n)$ norm when the damping is localized. In addition, when the dissipative mechanism acts on the whole space $\mathbb{R}^n$, we prove the exponential decay of the $H^1(\mathbb{R}^n)$ norm. Our strategy of proof combines a Kato's type smoothing effect, unique continuation and an observability inequality. |
| title | On the stabilization of $L^2$ and $H^1$ norms for the Zakharov-Kuznetsov equation with damping |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.16441 |