http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
NONRELATIVISTIC LIMIT IN THE SELF-DUAL ABELIAN CHERN-SIMONS MODEL
Han, Jong-Min,Song, Kyung-Woo Korean Mathematical Society 2007 대한수학회지 Vol.44 No.4
We consider the nonrelativistic limit in the self-dual Abelian Chern-Simons model, and give a rigorous proof of the limit for the radial solutions to the self-dual equations with the nontopological boundary condition when there is only one-vortex point. By keeping the shooting constant of radial solutions to be fixed, we establish the convergence of radial solutions in the nonrelativistic limit.
NONRELATIVISTIC LIMIT OF CHERN-SIMONS GAUGED FIELD EQUATIONS
Chae, Myeongju,Yim, Jihyun Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.3
We study the nonrelativistic limit of the Chern-Simons-Dirac system on ${\mathbb{R}}^{1+2}$. As the light speed c goes to infinity, we first prove that there exists an uniform existence interval [0, T] for the family of solutions ${\psi}^c$ corresponding to the initial data for the Dirac spinor ${\psi}_0^c$ which is bounded in $H^s$ for ${\frac{1}{2}}$ < s < 1. Next we show that if the initial data ${\psi}_0^c$ converges to a spinor with one of upper or lower component zero in $H^s$, then the Dirac spinor field converges, modulo a phase correction, to a solution of a linear $Schr{\ddot{o}}dinger$ equation in C([0, T]; $H^{s^{\prime}}$) for s' < s.
Choi, Woocheol,Hong, Younghun,Seok, Jinmyoung Elsevier 2018 Journal of functional analysis Vol.274 No.3
<P><B>Abstract</B></P> <P>In this paper, we are concerned with the nonrelativistic limit of the following pseudo-relativistic equation with Hartree nonlinearity or power type nonlinearity [FORMULA OMISSION] where <I>c</I> denotes the speed of light. We prove that as c → ∞ the ground states of this equation converges to the ground state of its nonrelativistic counterpart [FORMULA OMISSION] with convergence rate 1 / <SUP> c 2 </SUP> in every <SUP> H s </SUP> norms. Moreover, we show that this rate is optimal.</P>
LOW REGULARITY SOLUTIONS TO HIGHER-ORDER HARTREE-FOCK EQUATIONS WITH UNIFORM BOUNDS
Changhun Yang(Changhun Yang) 충청수학회 2024 충청수학회지 Vol.37 No.1
In this paper, we consider the higher-order Hartree-Fock equations. The higher-order linear Schr¨odinger equation was introduced in [5] as the formal finite Taylor expansion of the pseudo-relativistic linear Schr¨odinger equation. In [13], the authors established global-in-time Strichartz estimates for the linear higher-order equations which hold uniformly in the speed of light c ≥ 1 and as their applications they proved the convergence of higher-order Hartree-Fock equations to the corresponding pseudo-relativistic equation on arbitrary time interval as c goes to infinity when the Taylor expansion order is odd. To achieve this, they not only showed the existence of solutions in L2 space but also proved that the solutions stay bounded uniformly in c