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arXiv · 2410.11266

Complex-valued solutions of the mKdV equations in generalized Fourier-Lebesgue spaces

Zijun Chen·Zihua Guo·Chunyan Huang
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Abstract

We study the \emph{complex-valued} solutions to the Cauchy problem of the modified Korteweg-de Vries equation on the real line. To study the low-regularity problems, we employ a generalized Fourier-Lebesgue space $\widehat{M}^{s}_{r,q}(\mathbb{R})$ that unifies the modulation spaces and the Fourier-Lebesgue spaces. We then prove sharp local well-posedness results in this space by perturbation arguments using $X^{s,b}$-type spaces. Our results improve the previous one in \cite{GV}.

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Zijun Chen, Zihua Guo, Chunyan Huang. 2024-10-15. Complex-valued solutions of the mKdV equations in generalized Fourier-Lebesgue spaces. https://doi.org/10.1090/proc%2F17114

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