Volume 15, Issue 2
Semiclassical Limit of Nonlinear Schrodinger Equation (II)

Ping Zhang

DOI:

J. Part. Diff. Eq., 15 (2002), pp. 83-96.

Published online: 2002-05

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  • Abstract

In this paper, we use the Wigner measure approach to study the semiclassical limit of nonlinear Schrödinger equation in small time. We prove that: the limits of the quantum density: ρ^∈ =: |ψ^∈|² and the quantum momentum: J^∈ =: ∈Im(\overline{ψ^∈}∇ψ^∈) satisfy the compressible Euler equations before the formation of singularities in the limit system.

  • Keywords

Schrödinger compressible Euler Wigner transformation Wigner Measure

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@Article{JPDE-15-83, author = {}, title = {Semiclassical Limit of Nonlinear Schrodinger Equation (II)}, journal = {Journal of Partial Differential Equations}, year = {2002}, volume = {15}, number = {2}, pages = {83--96}, abstract = { In this paper, we use the Wigner measure approach to study the semiclassical limit of nonlinear Schrödinger equation in small time. We prove that: the limits of the quantum density: ρ^∈ =: |ψ^∈|² and the quantum momentum: J^∈ =: ∈Im(\overline{ψ^∈}∇ψ^∈) satisfy the compressible Euler equations before the formation of singularities in the limit system.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5450.html} }
TY - JOUR T1 - Semiclassical Limit of Nonlinear Schrodinger Equation (II) JO - Journal of Partial Differential Equations VL - 2 SP - 83 EP - 96 PY - 2002 DA - 2002/05 SN - 15 DO - http://dor.org/ UR - https://global-sci.org/intro/jpde/5450.html KW - Schrödinger KW - compressible Euler KW - Wigner transformation KW - Wigner Measure AB - In this paper, we use the Wigner measure approach to study the semiclassical limit of nonlinear Schrödinger equation in small time. We prove that: the limits of the quantum density: ρ^∈ =: |ψ^∈|² and the quantum momentum: J^∈ =: ∈Im(\overline{ψ^∈}∇ψ^∈) satisfy the compressible Euler equations before the formation of singularities in the limit system.
Ping Zhang . (2019). Semiclassical Limit of Nonlinear Schrodinger Equation (II). Journal of Partial Differential Equations. 15 (2). 83-96. doi:
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