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arXiv · 2511.17471

Growth of Fourier--Lebesgue norms for mKdV

Saikatul Haque·Rowan Killip·Monica Visan·Yunfeng Zhang
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Abstract

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.

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Saikatul Haque, Rowan Killip, Monica Visan, Yunfeng Zhang. 2025-11-21. Growth of Fourier--Lebesgue norms for mKdV. https://arxiv.org/abs/2511.17471

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