A Note on the Local Well-Posedness for the Whitham Equation

DOI10.1007/978-3-319-12547-3_3zbMath1326.35312OpenAlexW2188293074MaRDI QIDQ3447498

Joachim Escher, Long Pei, Mats Ehrnström

Publication date: 27 October 2015

Published in: Elliptic and Parabolic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-12547-3_3

zbMATH Keywords

Whitham equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)

Related Items (16)

Instability and nonuniqueness for the \(b\)-Novikov equation ⋮ Ill-posedness for the \(b\)-family of equations ⋮ Construction of 2-Peakon Solutions and Ill-Posedness for the Novikov Equation ⋮ Modulational instability in the Whitham equation with surface tension and vorticity ⋮ Existence of a weak solution and blow-up of strong solutions for a two-component Fornberg-Whitham system ⋮ Existence of a highest wave in a fully dispersive two-way shallow water model ⋮ Symmetry and decay of traveling wave solutions to the Whitham equation ⋮ Rigorous derivation of the Whitham equations from the water waves equations in the shallow water regime ⋮ Classical well-posedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces ⋮ A note on well-posedness of bidirectional Whitham equation ⋮ Solitary wave solutions of a Whitham-Boussinesq system ⋮ Small amplitude traveling waves in the full-dispersion Whitham equation ⋮ Solitary waves in dispersive evolution equations of Whitham type with nonlinearities of mild regularity ⋮ The well-posedness, blow-up, and traveling waves for a two-component Fornberg–Whitham system ⋮ On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation ⋮ Existence of solitary-wave solutions to nonlocal equations

Cites Work

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• Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations
• On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type
• Global Bifurcation for the Whitham Equation
• Dispersive Perturbations of Burgers and Hyperbolic Equations I: Local Theory
• Variational methods and applications to water waves

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