期刊
TAIWANESE JOURNAL OF MATHEMATICS
卷 4, 期 4, 页码 501-529出版社
MATHEMATICAL SOC REP CHINA
DOI: 10.11650/twjm/1500407291
关键词
dispersive limit; quantum hydrodynamics; KdV equation; Wigner transform; compressible Euler equation
类别
In this review paper we present the most important mathematical properties of dispersive limits of (non)linear Schrodinger type equations. Different formulations are used to study these singular limits, e.g., the kinetic formulation of the linear Schrodinger equation based on the Wigner transform is well suited for global-in-time analysis without using WKB-(expansion) techniques, while the modified Madelung transformation reformulating Schrodinger equations in terms of a dispersive perturbation of a quasilinear symmetric hyperbolic system usually only gives local-in-time results due to the hyperbolic nature of the limit equations. Deterministic analogues of turbulence are also discussed. There, turbulent diffusion appears naturally in the zero dispersion limit.
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