Growth of Fourier--Lebesgue norms for mKdV
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911278873706496 |
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| author | Haque, Saikatul Killip, Rowan Visan, Monica Zhang, Yunfeng |
| author_facet | Haque, Saikatul Killip, Rowan Visan, Monica Zhang, Yunfeng |
| contents | We demonstrate inflation of Fourier--Lebesgue norms for solutions to the focusing modified Korteweg--de Vries equation posed on the real line. For $p\neq 2$ and all $s\in \mathbb{R}$, we construct a sequence of solutions $u_n$ whose initial data $u_n(0)$ converges to zero in the Fourier--Lebesgue spaces $\mathcal F L^p_s(\mathbb{R})$, but whose evolutions at later times $t_n$ diverge to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17471 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Growth of Fourier--Lebesgue norms for mKdV Haque, Saikatul Killip, Rowan Visan, Monica Zhang, Yunfeng Analysis of PDEs We demonstrate inflation of Fourier--Lebesgue norms for solutions to the focusing modified Korteweg--de Vries equation posed on the real line. For $p\neq 2$ and all $s\in \mathbb{R}$, we construct a sequence of solutions $u_n$ whose initial data $u_n(0)$ converges to zero in the Fourier--Lebesgue spaces $\mathcal F L^p_s(\mathbb{R})$, but whose evolutions at later times $t_n$ diverge to infinity. |
| title | Growth of Fourier--Lebesgue norms for mKdV |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.17471 |