Global existence for a nonlinear Schrödinger-Chern-Simons system on a surface. (English) Zbl 1166.35035

Demoulini, Sophia

Ann. Inst. Henri Poincaré, Anal. Non Linéaire 24, No. 2, 207-225 (2007).

The author establish global existence of regular solutions to a nonlinear Schrödinger-Chern-Simons system of equations over a two-dimensional compact Riemannian manifold.

Reviewer: Dian K. Palagachev (Bari)

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
58J05	Elliptic equations on manifolds, general theory

Keywords:

Nonlinear Schrödinger; Chern-Simons system; Global existence; Regularity; Riemannian manifold

References:

[1]	Aubin, T., Nonlinear Analysis on Manifolds. Monge-Ampere Equations (1980), Springer-Verlag: Springer-Verlag New York
[2]	Berge, L.; de Bouard, A.; Saut, J., Blowing up time-dependent solutions of the planar Chern-Simons gauged nonlinear Schrodinger equation, Nonlinearity, 8, 235-253 (1995) · Zbl 0822.35125
[3]	Berge, L.; de Bouard, A.; Saut, J., Collapse of Chern-Simons-gauged matter fields, Phys. Rev. Lett., 74, 3907-3911 (1995) · Zbl 1020.81698
[4]	Brezis, H.; Gallouet, T., Nonlinear Schroedinger evolution equations, Nonlinear Anal., 4, 4, 677-681 (1980) · Zbl 0451.35023
[5]	Chae, D.; Choe, K., Global existence in the Cauchy problem of the relativistic Chern-Simons-Higgs theory, Nonlinearity, 15, 747-758 (2002) · Zbl 1073.58014
[6]	Demoulini, S.; Stuart, D., Gradient flow of the superconducting Ginzburg-Landau functional on the plane, Comm. Anal. Geom., 5, 1, 121-198 (1997) · Zbl 0894.35107
[7]	Demoulini, S., Periodic solutions and rigid rotation of the gauged Ginzburg-Landau vortices, ((Berlin, 1999). (Berlin, 1999), International Conference on Differential Equations, vols. 1,2 (2000), World Sci. Publishing: World Sci. Publishing River Edge, NJ), 542-544 · Zbl 0969.35122
[8]	Kato, T., Linear evolution equations of “hyperbolic” type, J. Fac. Sci. Univ. Tokyo Sect. I, 17, 241-258 (1970) · Zbl 0222.47011
[9]	Majda, A., Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Sciences, vol. 53 (1984), Springer-Verlag · Zbl 0537.76001
[10]	Manton, N., First order vortex dynamics, Ann. Phys., 256, 114-131 (1997) · Zbl 0932.58014
[11]	Palais, R., Foundations of Global Nonlinear Analysis, Mathematics Lecture Note Series (1968), W.A. Benjamin: W.A. Benjamin New York · Zbl 0164.11102
[12]	Stuart, D., Dynamics of Abelian Higgs vortices in the near Bogomolny regime, Comm. Math. Phys., 159, 51-91 (1994) · Zbl 0807.35141
[13]	Stuart, D., Periodic solutions of the Abelian Higgs model and rigid rotation of vortices, Geom. Funct. Anal. (GAFA), 9, 1-28 (1999)
[14]	Taylor, M., Partial Differential Equations, Applied Mathematical Sciences, vol. 117 (1996), Springer-Verlag