Well-posedness and weak rotation limit for the Ostrovsky equation

DOI10.1016/j.jde.2009.09.009zbMath1181.35253OpenAlexW2058033860MaRDI QIDQ1040603

Kotaro Tsugawa

Publication date: 25 November 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.09.009

zbMATH Keywords

Cauchy problemwell-posednessKdV equationOstrovsky equationFourier restriction normlow regularityweak rotation limit

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (27)

The Cauchy problem for the generalized Ostrovsky equation with negative dispersion ⋮ High-frequency instabilities of the Ostrovsky equation ⋮ The Cauchy problem for quadratic and cubic Ostrovsky equation with negative dispersion ⋮ Well-posedness and dispersive/diffusive limit of a generalized Ostrovsky-Hunter equation ⋮ Asymptotics for the Ostrovsky-Hunter equation in the critical case ⋮ Validity of the Weakly Nonlinear Solution of the Cauchy Problem for the Boussinesq-Type Equation ⋮ Global existence of small-norm solutions in the reduced Ostrovsky equation ⋮ On the stability of solitary waves of a generalized Ostrovsky equation ⋮ Well-posedness of bounded solutions of the non-homogeneous initial-boundary value problem for the Ostrovsky–Hunter equation ⋮ Dispersive and diffusive limits for Ostrovsky-Hunter type equations ⋮ Existence, regularity and symmetry of periodic traveling waves for Gardner-Ostrovsky type equations ⋮ Sharp well-posedness of the Cauchy problem for a generalized Ostrovsky equation with positive dispersion ⋮ Stability of Solitary Waves of the Kadomtsev--Petviashvili Equation with a Weak Rotation ⋮ Stability of constrained solitary waves for the Ostrovsky-Vakhnenko model in the coastal zone ⋮ On a model for internal waves in rotating fluids ⋮ On the solutions for an Ostrovsky type equation ⋮ Convergence of the Ostrovsky equation to the Ostrovsky-Hunter one ⋮ Oleinik type estimates for the Ostrovsky-Hunter equation ⋮ Well-posedness of the Ostrovsky-Hunter equation under the combined effects of dissipation and short-wave dispersion ⋮ A convergent finite difference scheme for the Ostrovsky-Hunter equation on a bounded domain ⋮ Symmetry and uniqueness of the solitary-wave solution for the Ostrovsky equation ⋮ White noise driven Ostrovsky equation ⋮ The Cauchy problem for the Ostrovsky equation with positive dispersion ⋮ Solitary waves of a generalized Ostrovsky equation ⋮ Continuity properties of the solution map for the generalized reduced Ostrovsky equation ⋮ Some Wellposedness Results for the Ostrovsky–Hunter Equation ⋮ The Cauchy problem for the Ostrovsky equation with negative dispersion at the critical regularity

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