zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

35Q55NLS-like (nonlinear Schrödinger) equations
58J05Elliptic equations on manifolds, general theory
Full Text: DOI EuDML
[1] Aubin, T.: Nonlinear analysis on manifolds. Monge -- Ampère equations. (1980) · Zbl 0512.53044
[2] Berge, L.; De Bouard, A.; Saut, J.: Blowing up time-dependent solutions of the planar Chern -- Simons gauged nonlinear Schrödinger 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, No. 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, No. 1, 121-198 (1997) · Zbl 0894.35107
[7] Demoulini, S.: Periodic solutions and rigid rotation of the gauged Ginzburg -- Landau vortices. International conference on differential equations, vols. 1,2, 542-544 (2000) · 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 53 (1984) · 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) · 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) · Zbl 0998.35053
[14] Taylor, M.: Partial differential equations. Applied mathematical sciences 117 (1996) · Zbl 0869.35001