On persistence of spatial analyticity for the dispersion-generalized periodic KdV equation. (December 2017)

• Record Type: Journal Article
• Authors: Himonas, A. Alexandrou; Kalisch, Henrik; Selberg, Sigmund
• Is Part Of: Nonlinear analysis. Volume 38(2017)
• Page Start: 35
• Page End: 48
• Publication Date: 2017-12
• Subjects: Bourgain spaces -- Gevrey regularity -- Radius of analyticity -- KdV equation -- Algebraic decrease; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.04.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Persistence of spatial analyticity is studied for periodic solutions of the dispersion-generalized KdV equation u t − | D x | α u x + u u x = 0 for α ≥ 2 . For a class of analytic initial data with a uniform radius of analyticity σ 0 > 0, we obtain an asymptotic lower bound σ ( t ) ≥ c t − p on the uniform radius of analyticity σ ( t ) at time t, as t → ∞, where p = max ( 1, 4 / α ) . The proof relies on bilinear estimates in Bourgain spaces and an approximate conservation law.