Existence and uniqueness of the global conservative weak solutions for the integrable Novikov equation

DOI10.1512/iumj.2018.67.7510zbMath1501.35003arXiv1509.08569OpenAlexW2963992496WikidataQ128749761 ScholiaQ128749761MaRDI QIDQ3120778

Geng Chen, Robin Ming Chen, Yue Liu

Publication date: 19 March 2019

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.08569

zbMATH Keywords

uniquenessglobal weak solutionintegrable systemCamassa-Holm equationNovikov equation

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for nonlinear higher-order PDEs (35G25) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (18)

Stability of peakons of the Camassa–Holm equation beyond wave breaking ⋮ Ghostpeakons and characteristic curves for the Camassa-Holm, Degasperis-Procesi and Novikov equations ⋮ A Riemann-Hilbert approach for the Novikov equation ⋮ Lipschitz metric for the Novikov equation ⋮ Existence and regularity for global weak solutions to the 𝜆-family water wave equations ⋮ Globally conservative weak solutions for a class of nonlinear dispersive wave equations beyond wave breaking ⋮ Blow-up analysis for the \(ab\)-family of equations ⋮ Curvature blow-up and peakons for the Camassa-Holm type equation ⋮ On conservative sticky peakons to the modified Camassa-Holm equation ⋮ Existence and uniqueness of the global conservative weak solutions for a cubic Camassa-Holm type equation ⋮ Existence and uniqueness of the global conservative weak solutions to the cubic Camassa-Holm-type equation ⋮ Existence and uniqueness of the global conservative weak solutions to the rotation-Camassa-Holm equation ⋮ Blow-up phenomena and peakons for the gFQXL/gCH-mCH equation ⋮ Non-uniform dependence and well-posedness for the rotation-Camassa-Holm equation on the torus ⋮ Qualitative analysis for a new generalized 2-component Camassa-Holm system ⋮ A view of the peakon world through the lens of approximation theory ⋮ Non-uniform dependence on initial data for the rotation-Camassa-Holm equation ⋮ Global weak solutions to the Novikov equation by viscous approximation

Cites Work

• Unnamed Item
• Unnamed Item
• Lipschitz metric for the Camassa-Holm equation on the line
• Uniqueness of conservative solutions to the Camassa-Holm equation via characteristics
• Lipschitz metric for the periodic Camassa-Holm equation
• Traveling wave solutions for a class of one-dimensional nonlinear shallow water wave models
• Global semigroup of conservative solutions of the nonlinear variational wave equation
• Global conservative solutions of the Camassa-Holm equation
• An optimal transportation metric for solutions of the Camassa-Holm equation
• Conservative solutions to a nonlinear variational wave equation
• Wave breaking for nonlinear nonlocal shallow water equations
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
• Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• Existence and regularity of solutions in nonlinear wave equations
• Unique conservative solutions to a variational wave equation
• On the weak solutions to a shallow water equation
• Global well-posedness for the periodic Novikov equation with cubic nonlinearity
• GENERALIZED CHARACTERISTICS AND THE HUNTER–SAXTON EQUATION
• Global weak solutions for the Novikov equation
• GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Integrable peakon equations with cubic nonlinearity
• Generalizations of the Camassa–Holm equation
• An integrable shallow water equation with peaked solitons
• ON THE UNIQUENESS AND LARGE TIME BEHAVIOR OF THE WEAK SOLUTIONS TO A SHALLOW WATER EQUATION
• Integrable equations arising from motions of plane curves

This page was built for publication: Existence and uniqueness of the global conservative weak solutions for the integrable Novikov equation