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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 12 <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\"{o}dinger equation in $C([0, T]; H^{s'})$ for $ s' <s $.
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참고문헌 (12)
참고문헌 신청
P. Bechouche / 2004 / Nonrelativistic limit of Klein-Gordon-Maxwell to Schrodinger-Poisson / Amer. J. Math. 126(1):31~64
P. Bechouche / 2005 / On the asymptotic analysis of the Dirac-Maxwell system in the nonrelativistic limit / J. Hyperbolic Differ. Equ. 2(1):129~182
N. Bournaveas / 2014 / A note on the Chern-Simons-Dirac equations in the Coulomb gauge / Discrete Contin. Dyn. Syst. 34(7):2693~2701
M. Chae / 2009 / Semi-nonrelativistic limit of the Chern-Simons-Higgs system / J. Math. Phys. 50(7):19
J.-Y. Chemin / 1998 / Perfect incompressible fluids, translated from the 1995 French original by Isabelle Gallagher and Dragos Iftimie, Oxford Lecture Series in Mathematics and its Applications / The Clarendon Press, Oxford University Press :14
P. Bechouche / 2005 / On the asymptotic analysis of the Dirac-Maxwell system in the nonrelativistic limit / J. Hyperbolic Differ. Equ. 2(1):129~182
N. Bournaveas / 2014 / A note on the Chern-Simons-Dirac equations in the Coulomb gauge / Discrete Contin. Dyn. Syst. 34(7):2693~2701
M. Chae / 2009 / Semi-nonrelativistic limit of the Chern-Simons-Higgs system / J. Math. Phys. 50(7):19
J.-Y. Chemin / 1998 / Perfect incompressible fluids, translated from the 1995 French original by Isabelle Gallagher and Dragos Iftimie, Oxford Lecture Series in Mathematics and its Applications / The Clarendon Press, Oxford University Press :14
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