Incompressible and compressible limits of coupled systems of nonlinear Schrödinger equations

DOI10.1007/s00220-006-0061-xzbMath1123.35071OpenAlexW2092367601MaRDI QIDQ881638

Tai-Chia Lin, Ping Zhang

Publication date: 31 May 2007

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-006-0061-x

zbMATH Keywords

shock wavesLyapunov functionalinterface dynamicsbinary mixture of Bose-Einstein condensatesdouble condensate

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Statistical mechanics of superfluids (82D50) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Initial value problems for nonlinear higher-order PDEs (35G25)

Related Items

Asymptotic limit of the Gross-Pitaevskii equation with general initial data ⋮ Hydrodynamic limits of the nonlinear Schrödinger equation with the Chern-Simons gauge fields ⋮ Semiclassical analysis with new Galilean transformations for a Gross-Pitaevskii system with nonzero conditions at infinity ⋮ Hydrodynamic limits of Manton's Schrödinger system ⋮ Rotating multicomponent Bose-Einstein condensates ⋮ Quantified hydrodynamic limits for Schrödinger-type equations without the nonlinear potential ⋮ Global minimizers of coexistence for rotating \(N\)-component Bose-Einstein condensates ⋮ The spatial behavior of rotating two-component Bose-Einstein condensates ⋮ Low Froude number limit of the rotating shallow water and Euler equations ⋮ Two-component Bose-Einstein condensates ⋮ Phase separation of two-component Bose–Einstein condensates ⋮ Bose-Einstein condensates with non-classical vortex ⋮ Rotating two-component Bose-Einstein condensates ⋮ Sharp thresholds of two-components Bose-Einstein condensates ⋮ Hydrodynamic limits of the nonlinear Klein-Gordon equation ⋮ Inviscid, zero Froude number limit of the viscous shallow water system ⋮ Incompressible and compressible limits of two-component Gross–Pitaevskii equations with rotating fields and trap potentials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compressible fluid flow and systems of conservation laws in several space variables
• Semiclassical limit of the Gross-Pitaevskii equation in an exterior domain
• Formation of singularities in three-dimensional compressible fluids
• Data dependence in the mathematical theory of compressible inviscid fluids
• On the incompressible fluid limit and the vortex motion law of the nonlinear Schrödinger equation
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Non-linear semi-groups
• Nonlinear Schrödinger evolution equations
• Semiclassical limit of the nonlinear Schrödinger equation in small time
• Wigner Measure and the Semiclassical Limit of Schrödinger--Poisson Equations
• CONVERGENCE OF THE SCHRÖDINGER–POISSON SYSTEM TO THE INCOMPRESSIBLE EULER EQUATIONS