The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces

DOI10.1016/j.anihpc.2012.06.006OpenAlexW2001384022MaRDI QIDQ2450595

Gustavo Ponce, Germán E. Fonseca, Felipe Linares

Publication date: 14 May 2014

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5967

zbMATH Keywords

Benjamin-Ono equationoptimal decay ratepersistence results in weighted Sobolev spacessharp unique continuation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for nonlinear higher-order PDEs (35G25) Continuation and prolongation of solutions to PDEs (35B60)

Related Items (28)

Local well-posedness for a fractional KdV-type equation ⋮ On well-posedness for some dispersive perturbations of Burgers' equation ⋮ The generalized fractional Benjamin-Bona-Mahony equation: analytical and numerical results ⋮ The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in low regularity Sobolev spaces ⋮ Well-posedness for the two dimensional generalized Zakharov-Kuznetsov equation in anisotropic weighted Sobolev spaces ⋮ On persistence properties in fractional weighted spaces ⋮ The IVP for a nonlocal perturbation of the Benjamin-Ono equation in classical and weighted Sobolev spaces ⋮ Well-posedness for a two-dimensional dispersive model arising from capillary-gravity flows ⋮ On decay of the solutions for the dispersion generalized Benjamin-Ono and Benjamin-Ono equations ⋮ On the propagation of regularity and decay of solutions to the Benjamin equation ⋮ A reduced order modeling method based on GNAT-embedded hybrid snapshot simulation ⋮ Local well-posedness in weighted Sobolev spaces for nonlinear dispersive equations with applications to dispersive blow up ⋮ Asymptotic \(N\)-soliton-like solutions of the fractional Korteweg-de Vries equation ⋮ Traveling waves and transverse instability for the fractional Kadomtsev–Petviashvili equation ⋮ The IVP for a higher dimensional version of the Benjamin-Ono equation in weighted Sobolev spaces ⋮ On unique continuation for non-local dispersive models ⋮ Spatial decay properties for a model in shear flows posed on the cylinder ⋮ The Cauchy problem for dissipative Benjamin-Ono equation in weighted Sobolev spaces ⋮ Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE ⋮ On the unique continuation of solutions to non-local non-linear dispersive equations ⋮ Persistence properties for the dispersion generalized BO-ZK equation in weighted anisotropic Sobolev spaces ⋮ The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in weighted Sobolev spaces ⋮ The Zakharov-Kuznetsov equation in weighted Sobolev spaces ⋮ A note on the Ostrovsky equation in weighted Sobolev spaces ⋮ Asymptotic behavior of solutions of the dispersion generalized Benjamin-Ono equation ⋮ Enhanced Existence Time of Solutions to the Fractional Korteweg--de Vries Equation ⋮ On persistence properties in weighted spaces for solutions of the fractional Korteweg–de Vries equation ⋮ Well-posedness and ill-posedness results for the regularized Benjamin-Ono equation in weighted Sobolev spaces

Cites Work

• The sharp Hardy uncertainty principle for Schrödinger evolutions
• The IVP for the Benjamin-Ono equation in weighted Sobolev spaces
• Local well-posedness and blow-up in the energy space for a class of \(L^2\) critical dispersion generalized Benjamin-Ono equations
• Local well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spaces
• The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. II.
• Theory of Bessel potentials. I
• On the global well-posedness of the Benjamin-Ono equation
• On global well-posedness for a class of nonlocal dispersive wave equations
• On uniqueness properties of solutions of the \(k\)-generalized KdV equations
• Nonlocal models for nonlinear, dispersive waves
• Well-posedness for equations of Benjamin-Ono type
• Global well-posedness of Korteweg-de Vries equation in \(H^{-3/4}(\mathbb R)\)
• Solitary waves of nonlinear dispersive evolution equations with critical power nonlinearities
• Sur quelques généralisations de l'équation de Korteweg-de Vries
• Uniqueness and related analytic properties for the Benjamin-Ono equation -- A nonlinear Neumann problem in the plane
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• 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
• Unique continuation principles for the Benjamin-Ono equation
• Local well-posedness for dispersion-generalized Benjamin-Ono equations
• On well-posedness for the Benjamin-Ono equation
• Persistence properties and unique continuation of solutions of the Camassa-Holm equation
• Ill-Posedness Issues for the Benjamin--Ono and Related Equations
• Algebraic Solitary Waves in Stratified Fluids
• A Para-Differential Renormalization Technique for Nonlinear Dispersive Equations
• Global well-posedness of the Benjamin–Ono equation in low-regularity spaces
• On the decay properties of solutions to a class of Schrödinger equations
• On the Persistent Properties of Solutions to Semi-Linear Schrödinger Equation
• On the cauchy problem for the benjamin-ono equation
• Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
• The initial-value problem for the Korteweg-de Vries equation
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• A bilinear estimate with applications to the KdV equation
• The characterization of functions arising as potentials
• Internal waves of permanent form in fluids of great depth
• COMMUTATORS OF SINGULAR INTEGRAL OPERATORS
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces