×

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

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

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
58J05 Elliptic equations on manifolds, general theory
PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[1] Aubin, T., Nonlinear analysis on manifolds. monge – ampere equations, (1980), 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, (), 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 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.