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Zbl 0930.35154
Fonseca, German; Linares, Felipe; Ponce, Gustavo
Global well-posedness for the modified Korteweg-de Vries equation.
(English)
[J] Commun. Partial Differ. Equations 24, No.3-4, 683-705 (1999). ISSN 0360-5302; ISSN 1532-4133/e

The initial value problem (IVP) for the modified Korteweg-de Vries equation $$\partial_tu+ \partial^3_x u+ u^2 \partial_x u= 0$$ is studied. The global well-posedness of the IVP is studied in the classical Sobolev spaces $H^s(\bbfR)$. The main result $(s>3/5)$ combines the sharp local existence theory and its proof by Kenig-Ponce-Vega, and the dual version of the local smoothing effect. The result establishes that the IVP is globally well-posed in $H^s(\bbfR)$ with $s>3/5$.
MSC 2000:
*35Q53 KdV-like equations
35A05 General existence and uniqueness theorems (PDE)

Keywords: global well-posedness; Sobolev spaces; local existence theory

Cited in: Zbl 1157.35472

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