Local well-posedness for the quantum Zakharov system in three and higher dimensions

DOI10.1142/S0219891621500077zbMath1480.35103OpenAlexW3201275501WikidataQ115245170 ScholiaQ115245170MaRDI QIDQ5018992

Isao Kato

Publication date: 27 December 2021

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

Full work available at URL: https://doi.org/10.1142/s0219891621500077

zbMATH Keywords

Bourgain spacelow regularityhigh frequency quantum Langmuir waveslow frequency quantum ion acoustic waves

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Initial value problems for systems of nonlinear higher-order PDEs (35G55)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On one dimensional quantum Zakharov system
• The fourth-order nonlinear Schrödinger limit for quantum Zakharov system
• Local well-posedness for quadratic nonlinear Schrödinger equations and the ``good Boussinesq equation.
• Convolutions of singular measures and applications to the Zakharov system
• Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation
• Low-regularity bilinear estimates for a quadratic nonlinear Schrödinger equation
• Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
• Local well-posedness for the Cauchy problem of the quadratic Schrödinger equation with nonlinearity \(\overline{u}^2\)
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• On the Cauchy and invariant measure problem for the periodic Zakharov system
• Periodic Korteweg-de Vries equation with measures as initial data
• On the Cauchy problem for the Zakharov system
• Low regularity global well-posedness for the quantum Zakharov system in \(1D\)
• Well-posedness for the Zakharov system with the periodic boundary condition
• Global well-posedness and the classical limit of the solution for the quantum Zakharov system
• An improved local well-posedness result for the one-dimensional Zakharov system
• Local well-posedness for the quantum Zakharov system in one spatial dimension
• Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems
• On the 2D Zakharov system withL²Schrödinger data
• Low regularity global well-posedness for the two-dimensional Zakharov system
• A bilinear estimate with applications to the KdV equation
• Global well-posedness and scattering for the quantum Zakharov system in 𝐿²

This page was built for publication: Local well-posedness for the quantum Zakharov system in three and higher dimensions