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Bibliographic Details
Main Authors: Chen, Zijun, Guo, Zihua, Huang, Chunyan
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.11266
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Table of Contents:
  • 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}.