The semi-nonrelativistic limit of Chern–Simons–Higgs system is considered. We obtain several uniform estimates with respect to the light speed c and show the convergence of the solution of Chern–Simons–Higgs system to the solution of Chern–Simons–Schrödinger equations.

1.
Bechouche
,
P.
,
Mauser
,
N.
, and
Poupaud
,
F.
, “
(Semi)-nonrelativistic limits of the Dirac equation with external time-dependent electromagnetic field
,”
Commun. Math. Phys.
197
,
405
(
1998
).
2.
Bechouche
,
P.
,
Mauser
,
N.
, and
Selberg
,
S.
, “
Nonrelativistic limit of Klein-Gordon-Maxwell to Schrödinger-Poisson
,”
Am. J. Math.
126
,
31
(
2004
).
3.
Bergé
,
L.
,
de Bouard
,
A.
, and
Saut
,
J. C.
, “
Blowing up time-dependent solutions of the planar Chern-Simons gauged nonlinear Schrödinger equation
,”
Nonlinearity
8
,
235
(
1995
).
4.
Bergé
,
L.
and
Colin
,
T.
, “
A singular pertubation problem for an envelope equation in plasma physics
,”
Physica D
84
,
437
(
1995
).
5.
Chae
,
D.
and
Choe
,
K.
, “
Global existence in the Cauchy problem of the relativistic Chern-Simons-Higgs theory
,”
Nonlinearity
15
,
747
(
2002
).
6.
Ginibre
,
J.
and
Velo
,
G.
, “
The Cauchy problem for coupled Yang-Mills and Scalar fields in the temporal gauge
,”
Commun. Math. Phys.
82
,
1
(
1981
).
7.
Han
,
J.
and
Song
,
K.
, “
Nonrelativistic limit in the self-dual Abelian Chern-Simons model
,”
J. Korean Math. Soc.
44
,
997
(
2007
).
8.
Hong
,
J.
,
Kim
,
P.
, and
Pac
,
P.
, “
Multivortex solutions of the Abelian Chern-Simons-Higgs theory
,
Phys. Rev. Lett.
64
,
2230
(
1990
).
9.
Huh
,
H.
, “
Low regularity solutions of the Chern-Simons-Higgs equations
,”
Nonlinearity
18
,
2581
(
2005
).
10.
Huh
,
H.
, “
Local and global solutions of the Chern-Simons-Higgs system
,”
J. Funct. Anal.
242
,
526
(
2007
).
11.
Jackiw
,
R.
and
Pi
,
S. -Y.
, “
Classical and quantal nonrelativistic Chern-Simons theory
,”
Phys. Rev. D
42
,
3500
(
1990
).
12.
Jackiw
,
R.
and
Pi
,
S.-Y.
, “
Soliton solutions to the gauged nonlinear Schrödinger equation on the plane
,”
Phys. Rev. Lett.
64
,
2969
(
1990
).
13.
Jackiw
,
R.
and
Weinberg
,
E.
, “
Self-dual Chern-Simons vortices
,”
Phys. Rev. Lett.
64
,
2234
(
1990
).
14.
Masmoudi
,
N.
and
Nakanishi
,
K.
, “
Nonrelativistic limit from Maxwell-Klein-Gordon and Maxwell-Dirac to Poisson-Schrödinger
,”
Int. Math. Res. Notices
2003
,
679
.
15.
Tsutsumi
,
M.
, “
Nonrelativistic approximation of nonlinear Klein-Gordon equations in two space dimensions
,”
Nonlinear Anal. Theory, Methods Appl.
8
,
637
(
1984
).
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