Well-posedness of KdV on \(H^{-1}(\mathbb T)\). (English) Zbl 1101.35367
Tschinkel, Yuri (ed.), Mathematisches Institut, Georg-August-Universität Göttingen: Seminars Winter Term 2003/2004.; Lecture notes from the seminars “Number theory”, “Algebraic geometry” and “Geometric methods in representation theory” held at the University of Göttingen, Göttingen, Germany, 2003–2004. Göttingen: Universitätsdrucke Göttingen (ISBN 3-930457-51-2/pbk). 151-155 (2004).
Summary: We survey recent progress in the study of analytic properties of solutions of the KdV equation.
C. E. Kenig, G. Ponce and L. Vega, A bilinear estimate with applications to the KdV equation, J. Am. Math. Soc. 9, No. 2, 573–603 (1996; Zbl 0848.35114)]; T. Kappeler and P. Topalov, Global well-posedness of KdV in \(H^{-1}(\mathbb{T},\mathbb{R})\), Duke Math. J. 135, No. 2, 327–360 (2006; Zbl 1106.35081); Global well-posedness of mKdV in \(L^2 (\mathbb T, \mathbb R)\), Commun. Partial Differ. Equations 30, No. 3, 435–449 (2005; Zbl 1080.35119); Riccati representation for elements in \(L_{0}^{2}(\mathbb T)\) and its applications, J. Math. Anal. Appl. 309, No. 2, 544–566 (2005; Zbl 1085.34067), abridged version in PLISKA, Stud. Math. Bulg. 15, 171–188 (2003)].
For the entire collection see [Zbl 1081.11001].
C. E. Kenig, G. Ponce and L. Vega, A bilinear estimate with applications to the KdV equation, J. Am. Math. Soc. 9, No. 2, 573–603 (1996; Zbl 0848.35114)]; T. Kappeler and P. Topalov, Global well-posedness of KdV in \(H^{-1}(\mathbb{T},\mathbb{R})\), Duke Math. J. 135, No. 2, 327–360 (2006; Zbl 1106.35081); Global well-posedness of mKdV in \(L^2 (\mathbb T, \mathbb R)\), Commun. Partial Differ. Equations 30, No. 3, 435–449 (2005; Zbl 1080.35119); Riccati representation for elements in \(L_{0}^{2}(\mathbb T)\) and its applications, J. Math. Anal. Appl. 309, No. 2, 544–566 (2005; Zbl 1085.34067), abridged version in PLISKA, Stud. Math. Bulg. 15, 171–188 (2003)].
For the entire collection see [Zbl 1081.11001].
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35-02 | Research exposition (monographs, survey articles) pertaining to partial differential equations |
