ON GLOBAL WELL-POSEDNESS OF THE MODIFIED KDV EQUATION IN MODULATION SPACES

被引：5

作者：

Oh, Tadahiro ^{[1
,2
]}

Wang, Yuzhao ^{[3
]}

机构：

[1] Univ Edinburgh, Sch Math, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh, Midlothian, Scotland

[2] Maxwell Inst Math Sci, James Clerk Maxwell Bldg,Kings Bldg, Edinburgh, Midlothian, Scotland

[3] Univ Birmingham, Sch Math, Watson Bldg, Birmingham B15 2TT, W Midlands, England

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2021年 / 41卷 / 06期

基金：

欧洲研究理事会;

关键词：

Modified KdV equation; well-posedness; modulation space; INTEGRABLE GROUP-REPRESENTATIONS; ILL-POSEDNESS; SOLITON-SOLUTIONS; CAUCHY-PROBLEM; LOCAL WELL;

D O I：

10.3934/dcds.2020393

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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-s(2,p) (R) for s >= 1/4 and 2 <= p < infinity. For s < 1/4, we show that the solution map for mKdV is not locally uniformly continuous in M-s(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-s(2,p) (R) for s >= 1/4 and 2 <= p < infinity.

引用

页码：2971 / 2992

页数：22

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