Global well-posedness of Kirchhoff systems

Almost global well-posedness of Kirchhoff equation with Gevrey data

Article history: Received 26 November 2016 Accepted after revision 3 April 2017 Available online 18 April 2017 Presented by the Editorial Board The aim of this note is to present the almost global well-posedness result for the Cauchy problem for the Kirchhoff equation with large data in Gevrey spaces. We also briefly discuss the corresponding results in bounded and in exterior domains. © 2017 A...

Global 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...

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