On global well-posedness of the modified KdV equation in modulation spaces

Tadahiro Oh, Yuzhao Wang

Research output: Contribution to journalArticlepeer-review

Abstract

We study well-posedness of the complex-valued modified KdV equation (mKdV) on the real line. In particular, we prove local well-posedness of mKdV in modulation spaces M^{2,p}(\R) for s≥ 1 and 2≤p<∞. For s< 1/4, we show that the solution map for mKdV is not locally uniformly continuous in M^{2,p}(\R). By combining this local well-posedness with our previous work (2018) on an a priori global-in-time bound for mKdV in modulation spaces, we also establish global well-posedness of mKdV in M^{2,p}(\R) for s≥ 1/4 and 2≤p<∞.
Original languageEnglish
Number of pages22
JournalDiscrete and Continuous Dynamical Systems - Series A
Early online date25 Jan 2021
DOIs
Publication statusE-pub ahead of print - 25 Jan 2021

Keywords

  • modified KdV equation
  • well-posedness
  • modulation space

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