The local well-posedness of the coupled Ostrovsky system with low regularity

DOI10.1016/j.nonrwa.2024.104166zbMATH Open1547.35688MaRDI QIDQ6608383

Wei-Feng Zhang, Ting Luo

Publication date: 19 September 2024

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

zbMATH Keywords

local well-posednessill-posednessbilinear estimatecoupled Ostrovsky equationsBourgain space

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) KdV equations (Korteweg-de Vries equations) (35Q53) Ill-posed problems for PDEs (35R25) Asymptotic expansions of solutions to PDEs (35C20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) PDEs in connection with geophysics (35Q86) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Geophysical flows (76U60)

Cites Work

• Unnamed Item
• The Cauchy problem for the Ostrovsky equation with positive dispersion
• Local and global well-posedness for the Ostrovsky equation
• Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation
• Cauchy problem for the Ostrovsky equation in spaces of low regularity
• Global Cauchy problem for the Ostrovsky equation
• Local well-posedness and quantitative ill-posedness for the Ostrovsky equation
• Global well-posedness of Korteweg-de Vries equation in \(H^{-3/4}(\mathbb R)\)
• A model system for strong interaction between internal solitary waves
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
• On the existence of stationary solitary waves in a rotating fluid
• Periodic Korteweg-de Vries equation with measures as initial data
• On strongly interacting internal solitary waves
• Low regularity solutions for the Kadomtsev-Petviashvili I equation
• Cauchy problem for the Ostrovsky equation
• On the Cauchy problem for a coupled system of KdV equations
• Local well-posedness of the coupled KdV-KdV systems on \(\mathbb{R}\)
• The Cauchy problem for the Ostrovsky equation with negative dispersion at the critical regularity
• On strongly interacting internal waves in a rotating ocean and coupled Ostrovsky equations
• Weak and Strong Interactions between Internal Solitary Waves
• On the Surface Waves in a Shallow Channel with an Uneven Bottom
• Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
• Approximate Analytical and Numerical Solutions of the Stationary Ostrovsky Equation
• A bilinear estimate with applications to the KdV equation
• Remark on the local ill-posedness for KdV equation
• On a model system for the oblique interaction of internal gravity waves
• The Cauchy Problem for the Kadomtsev-Petviashvili (KPII) Equation in Three Space Dimensions
• On the Cauchy Problem for the Ostrovsky Equation with Positive Dispersion
• LOW-REGULARITY SOLUTIONS FOR THE OSTROVSKY EQUATION
• Analytical and numerical studies of weakly nonlocal solitary waves of the rotation-modified Korteweg-de Vries equation

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