منابع مشابه
Local Well-posedness for the Periodic Korteweg-de Vries Equation in Analytic Gevrey Classes
Motivated by the work of Grujić and Kalisch, [Z. Grujić and H. Kalisch, Local well-posedness of the generalized Korteweg-de Vries equation in spaces of analytic functions, Differential and Integral Equations 15 (2002) 1325–1334], we prove the local well-posedness for the periodic KdV equation in spaces of periodic functions analytic on a strip around the real axis without shrinking the width of...
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The I-method in its first version as developed by Colliander et al. in [2] is applied to prove that the Cauchy-problem for the generalised Korteweg-de Vries equation of order three (gKdV-3) is globally well-posed for large real-valued data in the Sobolev space H(R → R), provided s > − 1 42 .
متن کاملGlobal Well-posedness of Nls-kdv Systems for Periodic Functions
We prove that the Cauchy problem of the Schrödinger-KortewegdeVries (NLS-KdV) system for periodic functions is globally well-posed for initial data in the energy space H1×H1. More precisely, we show that the nonresonant NLS-KdV system is globally well-posed for initial data in Hs(T) × Hs(T) with s > 11/13 and the resonant NLS-KdV system is globally wellposed with s > 8/9. The strategy is to app...
متن کاملGlobal Well-posedness for Periodic Generalized Korteweg-de Vries Equation
In this paper, we show the global well-posedness for periodic gKdV equations in the space H(T), s ≥ 1 2 for quartic case, and s > 5 9 for quintic case. These improve the previous results of Colliander et al in 2004. In particular, the result is sharp in the quartic case.
متن کاملSharp ill-posedness and well-posedness results for the KdV-Burgers equation: the periodic case
We prove that the KdV-Burgers is globally well-posed in H−1(T) with a solution-map that is analytic fromH−1(T) to C([0, T ];H−1(T)) whereas it is ill-posed in Hs(T), as soon as s < −1, in the sense that the flow-map u0 7→ u(t) cannot be continuous from H s(T) to even D′(T) at any fixed t > 0 small enough. In view of the result of Kappeler and Topalov for KdV it thus appears that even if the dis...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2012
ISSN: 0022-0396
DOI: 10.1016/j.jde.2012.08.024