Title: Hydrodynamic limits of the nonlinear Klein-Gordon equation
Authors: Lin, Chi-Kun
Wu, Kung-Chien
應用數學系
數學建模與科學計算所(含中心)
Department of Applied Mathematics
Graduate Program of Mathematical Modeling and Scientific Computing, Department of Applied Mathematics
Issue Date: 1-Sep-2012
Abstract: We perform the mathematical derivation of the compressible and incompressible Euler equations from the modulated nonlinear Klein-Gordon equation. Before the formation of singularities in the limit system, the nonrelativistic-semiclassical limit is shown to be the compressible Euler equations. If we further rescale the time variable, then in the semiclassical limit (the light speed kept fixed), the incompressible Euler equations are recovered. The proof involves the modulated energy introduced by Brenier (2000) [1]. (C) 2012 Elsevier Masson SAS. All rights reserved.
URI: http://dx.doi.org/10.1016/j.matpur.2012.02.002
http://hdl.handle.net/11536/16864
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2012.02.002
Journal: JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
Volume: 98
Issue: 3
Begin Page: 328
End Page: 345
Appears in Collections:Articles


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