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 < ∞.
|Number of pages||22|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|Publication status||Published - Jun 2021|
Bibliographical noteFunding 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.
© 2021 American Institute of Mathematical Sciences. All rights reserved.
- Modified KdV equation
- Modulation space
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics