Browsing by Author "Wu, Kung-Chien"

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An Asymptotic Limit of a Navier-Stokes System with Capillary Effects
(2014-07-01)
Juengel, Ansgar
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Lin, Chi-Kun
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Wu, Kung-Chien
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應用數學系
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數學建模與科學計算所(含中心)
A combined incompressible and vanishing capillarity limit in the barotropic compressible Navier-Stokes equations for smooth solutions is proved. The equations are considered on the two-dimensional torus with well prepared initial data. The momentum equation contains a rotational term originating from a Coriolis force, a general Korteweg-type tensor modeling capillary effects, and a density-dependent viscosity. The limiting model is the viscous quasi-geostrophic equation for the "rotated" velocity potential. The proof of the singular limit is based on the modulated energy method with a careful choice of the correction terms.
ANELASTIC APPROXIMATION OF THE GROSS-PITAEVSKII EQUATION FOR GENERAL INITIAL DATA
(2014)
Lin, Chi-Kun
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Wu, Kung-Chien
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應用數學系
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數學建模與科學計算所(含中心)
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Department of Applied Mathematics
We perform a rigorous analysis of the anelastic approximation for the Gross-Pitaevskii equation with x-dependent chemical potential. For general initial data and periodic boundary condition, we show that as epsilon -> 0, equivalently the Planck constant tends to zero, the density vertical bar psi(epsilon)vertical bar(2) converges toward the chemical potential rho(0)(x) and the velocity field converges to the anelastic system.
Convergence of the Klein-Gordon equation to the wave map equation with magnetic field
(2010-03-15)
Wu, Kung-Chien
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數學建模與科學計算所(含中心)
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Graduate Program of Mathematical Modeling and Scientific Computing, Department of Applied Mathematics
This paper is devoted to the proof of the convergence from the modulated cubic nonlinear defocusing Klein-Gordon equation with magnetic field to the wave map equation. More precisely, we discuss the nonrelativistic-semiclassical limit of the modulated cubic nonlinear Klein-Gordon equation with magnetic field where the Planck's constant h = epsilon and the speed of light c are related by c = epsilon(-alpha) for some alpha >= 1. When alpha = 1 the limit wave function satisfies the wave map with one extra term coming from the magnetic field. However, alpha > 1, the effect of the magnetic filed disappears and the limit is the typical wave map equation only. (C) 2009 Elsevier Inc. All rights reserved.
Hydrodynamic limits of the nonlinear Klein-Gordon equation
(2012-09-01)
Lin, Chi-Kun
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Wu, Kung-Chien
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應用數學系
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數學建模與科學計算所(含中心)
;
Department of Applied Mathematics
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.
ON THE FLUID DYNAMICAL APPROXIMATION TO THE NONLINEAR KLEIN-GORDON EQUATION
(2012-06-01)
Lin, Chi-Kun
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Wu, Kung-Chien
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應用數學系
;
數學建模與科學計算所(含中心)
;
Department of Applied Mathematics
We study the nonrelativistic, semiclassical and nonrelativistic-semiclassical limits of the (modulated) nonlinear Klein-Gordon equations from its hydrodynamical structure via WKB analysis. The nonrelativistic-semiclassical limit is proved rigorously by modulated energy method.
Quasineutral Limit of the Schrodinger-Poisson System in Coulomb Gauge
(2011)
Lin, Chi-Kun
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Wong, Yau-Shu
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Wu, Kung-Chien
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應用數學系
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數學建模與科學計算所(含中心)
The zero Debye length asymptotic of the Schrodinger-Poisson system in Coulomb gauge for ill-prepared initial data is studied. We prove that when the scaled Debye length lambda -> 0, the current density defined by the solution of the Schrodinger-Poisson system in the Coulomb gauge converges to the solution of the rotating incompressible Euler equation plus a fast singular oscillating gradient vector field.
Singular Limits of the Klein-Gordon Equation
(2010-08-01)
Lin, Chi-Kun
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Wu, Kung-Chien
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應用數學系
;
數學建模與科學計算所(含中心)
;
Department of Applied Mathematics
We establish the singular limits, including semiclassical, nonrelativistic and nonrelativistic-semiclassical limits, of the Cauchy problem for the modulated defocusing nonlinear Klein-Gordon equation. For the semiclassical limit, h -> 0, we show that the limit wave function of the modulated defocusing cubic nonlinear Klein-Gordon equation solves the relativistic wave map and the associated phase function satisfies a linear relativistic wave equation. The nonrelativistic limit, c -> infinity, of the modulated defocusing nonlinear Klein-Gordon equation is the defocusing nonlinear Schrodinger equation. The nonrelativistic-semiclassical limit, h -> 0, c = h (-alpha) -> infinity for some alpha > 0, of the modulated defocusing cubic nonlinear Klein-Gordon equation is the classical wave map for the limit wave function and a typical linear wave equation for the associated phase function.