Convergence of Nonlinear Schrödinger–Poisson Systems to the Compressible Euler Equations

DOI10.1081/PDE-120021184zbMath1044.35090OpenAlexW2061420522MaRDI QIDQ4707064

Ansgar Jüngel, Shu Wang

Publication date: 9 June 2003

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

Full work available at URL: https://doi.org/10.1081/pde-120021184

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) NLS equations (nonlinear Schrödinger equations) (35Q55) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

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Cites Work

• Unnamed Item
• Unnamed Item
• Compressible fluid flow and systems of conservation laws in several space variables
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• On Wigner measures
• Kinetic formulation of the isentropic gas dynamics and \(p\)-systems
• The Schrödinger-Poisson-\(X\alpha\) equation
• Quasi-neutral limit of a nonlinear drift diffusion model for semiconductors
• On the weak solutions to a shallow water equation
• The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model
• Sur la solution à support compact de l’equation d’Euler compressible
• H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations
• The three-dimensional wigner-poisson problem: Existence, uniqueness and approximation
• The semiclassical limit of the defocusing NLS hierarchy
• Homogenization limits and Wigner transforms
• Global existence of small solutions to nonlinear Schrödinger equations
• Wigner Measure and the Semiclassical Limit of Schrödinger--Poisson Equations
• THE CLASSICAL LIMIT OF A SELF-CONSISTENT QUANTUM-VLASOV EQUATION IN 3D
• The limit from the Schrödinger‐Poisson to the Vlasov‐Poisson equations with general data in one dimension
• On the hydrodynamic limit of Ginzburg‐Landau wave vortices
• Defect measures of the vlasov-poisson system in the quasineutral regime
• Oscillations in quasineutral plasmas
• convergence of the vlasov-poisson system to the incompressible euler equations