Global Well-Posedness and Limit Behavior for a Higher-Order Benjamin-Ono Equation

DOI10.1080/03605302.2012.683846zbMath1258.35179arXiv1111.0858OpenAlexW2011406916MaRDI QIDQ4902758

Luc Molinet, Didier Pilod

Publication date: 17 January 2013

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.0858

zbMATH Keywords

initial value problemBenjamin-Ono equationgauge transformation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Internal waves for incompressible inviscid fluids (76B55) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (8)

Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation ⋮ The third order Benjamin-Ono equation on the torus: well-posedness, traveling waves and stability ⋮ Well-posedness for KdV-type equations with quadratic nonlinearity ⋮ Reducibility of a class of operators induced by the dispersive third order Benjamin-Ono equation ⋮ Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE ⋮ Local well-posedness for fourth order Benjamin-Ono type equations ⋮ IST Versus PDE: A Comparative Study ⋮ Modified energy method and applications for the well-posedness for the higher-order Benjamin-Ono equation and the higher-order intermediate long wave equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Well-posedness for a higher-order Benjamin-Ono equation
• Uniform well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation
• Global well-posedness in the energy space for the Benjamin-Ono equation on the circle
• Nonlocal models for nonlinear, dispersive waves
• Asymptotic models for internal waves
• Global well-posedness of the KP-I initial-value problem in the energy space
• On the Cauchy problem for higher-order nonlinear dispersive equations
• Global well-posedness and inviscid limit for the Korteweg-de Vries-Burgers equation
• On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations
• The Cauchy problem for the Benjamin-Ono equation in \(L^{2}\) revisited
• On global existence and scattering for the wave maps equation
• Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
• Ill-Posedness Issues for the Benjamin--Ono and Related Equations
• Global well-posedness of the Benjamin–Ono equation in low-regularity spaces
• Global well-posedness in <i>L</i><sup xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for the periodic Benjamin-Ono equation
• On the cauchy problem for the benjamin-ono equation
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H¹(R)
• Solitary-Wave Solutions of the Benjamin Equation
• Hamiltonian long‐wave expansions for free surfaces and interfaces

This page was built for publication: Global Well-Posedness and Limit Behavior for a Higher-Order Benjamin-Ono Equation