Periodic Cauchy problem for one two-dimensional generalization of the Benjamin–Ono equation in Sobolev spaces of low regularity. (November 2019)

• Record Type: Journal Article
• Authors: Bustamante, Eddye; Jiménez Urrea, José; Mejía, Jorge
• Is Part Of: Nonlinear analysis. Volume 188(2019)
• Page Start: 50
• Page End: 69
• Publication Date: 2019-11
• Subjects: 35Q53; Well-posedness -- Benjamin–Ono equation -- Sobolev spaces; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.05.014
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this work we prove that the initial value problem (IVP) associated to the two-dimensional Benjamin–Ono equation u t + H Δ u + u u x = 0, ( x, y ) ∈ T 2, t ∈ R, u ( x, y, 0 ) = u 0 ( x, y ), where H denotes the Hilbert transform with respect to the variable x and Δ is the Laplacian with respect to the spatial variables x and y, is locally well-posed in the periodic Sobolev space H s ( T 2 ), with s > 7 ∕ 4 .