A Para-Differential Renormalization Technique for Nonlinear Dispersive Equations

2009/07/27 by Sebastian Herr, Alexandru D. Ionescu, Carlos E. Kenig +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP #msc:35Q53

paper · pdf · doi:10.1080/03605302.2010.487232

published as Comm. Partial Differential Equations Vol. 35, No. 10, 1827-1875 (2010) · 42 pages, no figures

arxiv created 2009/07/27 · openalex publication_date 2010/09/01 · arxiv updated 2010/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

For α ∈ (1, 2) we prove that the initial-value problem is globally well-posed in the space of real-valued L 2-functions. We use a frequency dependent renormalization method to control the strong low-high frequency interactions.

Citations

• Local Well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spaces
• Sharp Global well-posedness for KdV and modified KdV on \R and \T

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