Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems

DOI10.1016/j.jfa.2015.06.008zbMath1331.35299OpenAlexW795836562MaRDI QIDQ892688

A. Alexandrou Himonas, Gerson Petronilho, Rafael F. Barostichi

Publication date: 11 November 2015

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2015.06.008

zbMATH Keywords

continuity of solution mapintegrable Camassa-Holm equationsOvsyannikov theorem for nonlocal equationswell-posedness of Cauchy problem in analytic spaces

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items

Analyticity in partial differential equations ⋮ A Cauchy-Kovalevsky Theorem for Nonlinear and Nonlocal Equations ⋮ The power series method for nonlocal and nonlinear evolution equations ⋮ A nonlocal transform to map and track quantum dynamics ⋮ The Cauchy problem for a 4-parameter family of equations with peakon traveling waves ⋮ Radius of analyticity for the Camassa-Holm equation on the line ⋮ Riemann-Hilbert approach for the FQXL model: A generalized Camassa-Holm equation with cubic and quadratic nonlinearity ⋮ Ill-posedness for the \(b\)-family of equations ⋮ On the Cauchy problem for a class of cubic quasilinear shallow-water equations ⋮ Local and global analyticity for \(\mu\)-Camassa-Holm equations ⋮ The global Gevrey regularity and analyticity of a two-component shallow water system with higher-order inertia operators ⋮ Multi-soliton solutions and the Cauchy problem for a two-component short pulse system ⋮ Local well-posedness and global analyticity for solutions of a generalized 0-equation ⋮ Analytic regularity of global solutions for the \(b\)-equation ⋮ Local and global analyticity for theμ-Novikov equation ⋮ Blow‐up of solutions for an integrable periodic two‐component Camassa‐Holm system with cubic nonlinearity ⋮ Local and Global Analyticity for a Generalized Camassa-Holm System ⋮ On well-posedness of nonlocal evolution equations ⋮ On the Cauchy problem for a four‐component Novikov system with peaked solutions ⋮ Evolution of the radius of spatial analyticity for the periodic BBM equation ⋮ On the Cauchy problem of a new integrable two-component Novikov equation ⋮ Stochastic differential equations in a scale of Hilbert spaces. Global solutions ⋮ The Cauchy problem and multi-peakons for the mCH-Novikov-CH equation with quadratic and cubic nonlinearities ⋮ Construction of peakon-antipeakon solutions and ill-posedness for the b-family of equations ⋮ Stochastic Camassa-Holm equation with convection type noise ⋮ Stochastic differential equations in a scale of Hilbert spaces ⋮ Global analyticity for a generalized Camassa-Holm equation and decay of the radius of spatial analyticity ⋮ A \(G^{\delta,1}\) almost conservation law for mCH and the evolution of its radius of spatial analyticity ⋮ Analyticity, Gevrey regularity and unique continuation for an integrable multi-component peakon system with an arbitrary polynomial function ⋮ Vector-valued measures of noncompactness and the Cauchy problem with delay in a scale of Banach spaces ⋮ A view of the peakon world through the lens of approximation theory

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Cauchy problem for the two-component Camassa-Holm system
• Non-uniform dependence on initial data for the CH equation on the line.
• On an integrable two-component Camassa-Holm shallow water system
• Traveling wave solutions for a class of one-dimensional nonlinear shallow water wave models
• On well-posedness of the Degasperis-Procesi equation
• Sharp estimates for analytic pseudodifferential operators and application to Cauchy problems
• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• The trajectories of particles in Stokes waves
• Global conservative solutions of the Camassa-Holm equation
• Non-uniform dependence on initial data of solutions to the Euler equations of hydrodynamics
• On a class of physically important integrable equations
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Sharp well-posedness results for the BBM equation
• Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa-Holm type equation
• Gain of regularity for equations of KdV type
• Remarks on the Korteweg-de Vries equation
• Solutions of the Korteweg-de Vries equation in fractional order Sobolev spaces
• A note on a theorem of Nirenberg
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
• Global existence for a new periodic integrable equation.
• On the Cauchy problem for an integrable equation with peakon solutions
• Analyticity of the Cauchy problem for an integrable evolution equation
• Construction of non-analytic solutions for the generalized KdV equation
• Traveling wave solutions of the Degasperis-Procesi equation
• On the ill-posedness of some canonical dispersive equations.
• The Cauchy problem for an integrable shallow-water equation
• A few remarks on the Camassa-Holm equation.
• Stability of the Camassa-Holm solitons
• Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
• Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
• The periodic Cauchy problem for the 2-component Camassa-Holm system.
• Non-uniform continuity in \(H^1\) of the solution map of the CH equation
• Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation
• An abstract form of the nonlinear Cauchy-Kowalewski theorem
• The Cauchy problem for the Fokas-Olver-Rosenau-Qiao equation
• Norm Inflation and Ill-Posedness for the Degasperis-Procesi Equation
• The Periodic Cauchy Problem for Novikov's Equation
• The initial value problem for a Novikov system
• On a Camassa–Holm type equation with two dependent variables
• An extension of integrable peakon equations with cubic nonlinearity
• A new integrable equation with cuspons and W/M-shape-peaks solitons
• Non-Uniform Dependence for the Periodic CH Equation
• Generalizations of the Camassa–Holm equation
• Remarks on the abstract form of nonlinear cauchy-kovalevsky theorems
• The inverse problem for periodic potentials
• A shallow water equation on the circle
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
• Perturbative symmetry approach
• An integrable shallow water equation with peaked solitons
• On Well-Posedness Results for Camassa-Holm Equation on the Line: A Survey
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• Particle trajectories in solitary water waves
• An Abstract Nonlinear Cauchy-Kovalevska Theorem
• The Cauchy problem for the Novikov equation
• On the Cauchy problem for the Camassa-Holm equation

This page was built for publication: Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems