Local and global well-posedness for the Ostrovsky equation
From MaRDI portal
Publication:818480
DOI10.1016/j.jde.2005.07.023zbMath1089.35061OpenAlexW2006076633MaRDI QIDQ818480
Aniura Milanés, Felipe Linares
Publication date: 20 March 2006
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2005.07.023
conservation lawsKP equationKorteweg-de Vries equationStrichartz estimatespropagation of surface waves in the ocean
Hydrology, hydrography, oceanography (86A05) KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)
Related Items
The Cauchy problem for the generalized Ostrovsky equation with negative dispersion ⋮ Invariant measure of stochastic damped Ostrovsky equation driven by pure jump noise ⋮ Mathematical analysis of a conservative numerical scheme for the Ostrovsky equation ⋮ Convergence problem of Ostrovsky equation with rough data and random data ⋮ High-frequency instabilities of the Ostrovsky equation ⋮ On the dimension of the divergence set 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 ⋮ Well-posedness of the Cauchy problem of Ostrovsky equation in anisotropic Sobolev spaces ⋮ Cauchy problem for the Ostrovsky equation in spaces of low regularity ⋮ 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 ⋮ The initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line ⋮ Solitary waves of a coupled KdV system with a weak rotation ⋮ Global existence of small-norm solutions in the reduced Ostrovsky equation ⋮ Global Cauchy problem for the 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 ⋮ Dispersive estimates for nonhomogeneous radial phases: an application to weakly dispersive equations and water wave models ⋮ Sharp well-posedness of the Cauchy problem for a generalized Ostrovsky equation with positive dispersion ⋮ Stability of constrained solitary waves for the Ostrovsky-Vakhnenko model in the coastal zone ⋮ On a model for internal waves in rotating fluids ⋮ The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves ⋮ 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 ⋮ Random attractors of the stochastic damped forced Ostrovsky 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 ⋮ A note on the Ostrovsky equation in weighted Sobolev spaces ⋮ On spatial discretization of evolutionary differential equations on the periodic domain with a mixed derivative ⋮ Global Well-Posedness of the Short-Pulse and Sine–Gordon Equations in Energy Space ⋮ Well‐posedness and unique continuation property for the generalized Ostrovsky equation with low regularity ⋮ Conservative numerical schemes for the Ostrovsky equation ⋮ Stability of solitary waves for the Ostrovsky equation ⋮ Symmetry and uniqueness of the solitary-wave solution for the Ostrovsky equation ⋮ White noise driven Ostrovsky equation ⋮ On the Cauchy Problem for the Ostrovsky Equation with Positive Dispersion ⋮ The Cauchy problem for the Ostrovsky equation with positive dispersion ⋮ Ergodicity of stochastic damped Ostrovsky equation driven by white noise ⋮ Well-posedness and unique continuation property for the solutions to the generalized Kawahara equation below the energy space ⋮ Local well-posedness and quantitative ill-posedness for the Ostrovsky equation ⋮ Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation ⋮ The global attractor of the viscous damped forced Ostrovsky equation ⋮ Continuity properties of the solution map for the generalized reduced Ostrovsky equation ⋮ Well-posedness and weak rotation limit for the Ostrovsky equation ⋮ Long time behavior of solutions to the damped forced generalized Ostrovsky equation below the energy space ⋮ Some Wellposedness Results for the Ostrovsky–Hunter Equation ⋮ The Cauchy problem for the Ostrovsky equation with negative dispersion at the critical regularity
Cites Work
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
- Cauchy problem for the Ostrovsky equation
- Global well-posedness for the KP-I equation
- Stability of solitary waves and weak rotation limit for the Ostrovsky equation
- Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
- On equations of KP-type
- Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
- A bilinear estimate with applications to the KdV equation
- Analytical and numerical studies of weakly nonlocal solitary waves of the rotation-modified Korteweg-de Vries equation
- Unnamed Item
- Unnamed Item
- Unnamed Item