Dilation method and smoothing effects of solutions to the Benjamin–Ono equation

DOI10.1017/S0308210500022733zbMath0847.35129MaRDI QIDQ4879060

Keiichi Kato, Tohru Ozawa, Nakao Hayashi

Publication date: 8 October 1996

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

Hilbert transformBenjamin-Ono equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items

Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity ⋮ Mixed initial-boundary value problem for the Benjamin-Ono equation ⋮ Intermediate long-wave equation on a half-line ⋮ Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE ⋮ Nonlinear smoothing and unconditional uniqueness for the Benjamin-Ono equation in weighted Sobolev spaces ⋮ Neumann initial-boundary value problem for Benjamin-Ono equation ⋮ Global existence and asymptotic behavior of solutions to the homogeneous Neumann problem for ILW equation on a half-line ⋮ Benjamin-Ono equation on a half-line ⋮ Interaction equations for short and long dispersive waves ⋮ Large time asymptotics of solutions to the generalized Benjamin-Ono equation ⋮ Mixed initial-boundary value problem for intermediate long-wave equation

Cites Work

• Regularity of solutions to nonlinear dispersive equations
• Nonlocal models for nonlinear, dispersive waves
• On solutions on the initial value problem for the nonlinear Schrödinger equations
• Weighted Sobolev spaces and rapidly decreasing solutions of some nonlinear dispersive wave equations
• The Benjamin-Ono equation in weighted Sobolev spaces
• Smoothing properties and existence of solutions for the generalized Benjamin-Ono equation
• On a class of nonlinear Schrödinger equations. II. Scattering theory, general case
• On solutions of the initial value problem for the nonlinear Schrödinger equations in one space dimension
• Regularity in time of solutions to nonlinear Schrödinger equations
• Algebraic Solitary Waves in Stratified Fluids
• On the cauchy problem for the benjamin-ono equation
• Benjamin—Ono-related equations and their solutions
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• On the Generalized Benjamin-Ono Equation
• Internal waves of permanent form in fluids of great depth