On Local Well posedness of the Schrödinger-Boussinesq Systems

DOI10.4208/jpde.v35.n4.5OpenAlexW4313059410WikidataQ115209369 ScholiaQ115209369MaRDI QIDQ5039966

Jie Shao, Bo-ling Guo

Publication date: 11 October 2022

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

Full work available at URL: https://doi.org/10.4208/jpde.v35.n4.5

zbMATH Keywords

Schrödinger-Boussinesq system Cauchy problem local wellposedness low regularity

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Second-order nonlinear hyperbolic equations (35L70) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Cites Work

• Local and global solutions for the non-linear Schrödinger-Boussinesq system.
• Local well-posedness for quadratic nonlinear Schrödinger equations and the ``good Boussinesq equation.
• Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation
• Low-regularity bilinear estimates for a quadratic nonlinear Schrödinger equation
• Scattering for the Gross-Pitaevskii equation
• The global solution of initial value problem for nonlinear Schrödinger- Boussinesq equation in 3-dimensions
• On the periodic Schrödinger-Boussinesq system
• Global existence of small solutions for a generalized Boussinesq equation
• On the Cauchy problem for the Zakharov system
• Counterexamples to bilinear estimates related with the KdV equation and the nonlinear Schrödinger equation
• Sharp local well-posedness for the ``good Boussinesq equation
• The Cauchy problem for Schrödinger-damped Boussinesq system
• Orbital stability of solitary waves of the Schrödinger-Boussinesq equation
• On Schrödinger-Boussinesq equations
• Local Solutions in Sobolev Spaces with Negative Indices for the “Good” Boussinesq Equation
• Quadratic forms for the 1-D semilinear Schrödinger equation
• Conservative finite difference methods for fractional Schrödinger–Boussinesq equations and convergence analysis

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