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

Tadahiro Oh, Yuzhao Wang

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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 Ms2,p(R) for s ≥ 14 and 2 ≤ p < ∞. For s < 14, we show that the solution map for mKdV is not locally uniformly continuous in Ms2,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 Ms2,p(R) for s ≥ 14 and 2 ≤ p < ∞.

Original languageEnglish
Pages (from-to)2971-2992
Number of pages22
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume41
Issue number6
DOIs
Publication statusPublished - Jun 2021

Bibliographical note

Funding Information:
The first author was supported by the European Research Council (grant no. 637995 “Prob-DynDispEq” and grant no. 864138 “SingStochDispDyn”). ∗ Corresponding author: Tadahiro Oh.

Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.

Keywords

  • Modified KdV equation
  • Modulation space
  • Well-posedness

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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