Concentration phenomena of two-vortex solutions in a Chern-Simons model
Chiun-Chuan Chen[1]; Chang-Shou Lin[2]; Guofang Wang[3]
- [1] Department of Mathematics Taiwan University Taipei, Taiwan
- [2] Department of Mathematics Chung-Cheng University Minghsiung, Chia-Yi 621 Taiwan
- [3] Max-Planck-Institute for Mathematics in the Sciences Inselstr. 22-26 04103 Leipzig, Germany
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2004)
- Volume: 3, Issue: 2, page 367-397
- ISSN: 0391-173X
Access Full Article
topAbstract
topHow to cite
topChen, Chiun-Chuan, Lin, Chang-Shou, and Wang, Guofang. "Concentration phenomena of two-vortex solutions in a Chern-Simons model." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.2 (2004): 367-397. <http://eudml.org/doc/84534>.
@article{Chen2004,
abstract = {By considering an abelian Chern-Simons model, we are led to study the existence of solutions of the Liouville equation with singularities on a flat torus. A non-existence and degree counting for solutions are obtained. The former result has an application in the Chern-Simons model.},
affiliation = {Department of Mathematics Taiwan University Taipei, Taiwan; Department of Mathematics Chung-Cheng University Minghsiung, Chia-Yi 621 Taiwan; Max-Planck-Institute for Mathematics in the Sciences Inselstr. 22-26 04103 Leipzig, Germany},
author = {Chen, Chiun-Chuan, Lin, Chang-Shou, Wang, Guofang},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {2},
pages = {367-397},
publisher = {Scuola Normale Superiore, Pisa},
title = {Concentration phenomena of two-vortex solutions in a Chern-Simons model},
url = {http://eudml.org/doc/84534},
volume = {3},
year = {2004},
}
TY - JOUR
AU - Chen, Chiun-Chuan
AU - Lin, Chang-Shou
AU - Wang, Guofang
TI - Concentration phenomena of two-vortex solutions in a Chern-Simons model
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2004
PB - Scuola Normale Superiore, Pisa
VL - 3
IS - 2
SP - 367
EP - 397
AB - By considering an abelian Chern-Simons model, we are led to study the existence of solutions of the Liouville equation with singularities on a flat torus. A non-existence and degree counting for solutions are obtained. The former result has an application in the Chern-Simons model.
LA - eng
UR - http://eudml.org/doc/84534
ER -
References
top- [1] L. Ahlfors, “Complex analysis”, 2nd edition, McGraw-Hill Book Co., New York, 1966. Zbl0395.30001MR510197
- [2] D. Bartolucci – G. Tarantello, Liouville type equations with singular data and their application to periodic multivortices for the electroweak theory, Comm. Math. Phys. 229 (2002), 3-47. Zbl1009.58011MR1917672
- [3] H. Brezis – F. Merle, Uniform estimates and blow-up behavior for solutions of in two dimensions, Comm. Partial Differential Equation 16 (1991), 1223-1253. Zbl0746.35006MR1132783
- [4] R. L. Bryant, Surfaces of mean curvature one in hyperbolic space, Astérisque 154-155 (1987), 321-347. Zbl0635.53047MR955072
- [5] L. Caffarelli – Y. Yang, Vortex condensation in the Chern-Simons Higgs model: an existence theorem, Comm. Math. Phys. 168 (1995), 321-336. Zbl0846.58063MR1324400
- [6] E. Caglioti – P. L. Lions – C. Marchioro – M. Pulvirenti, A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description, Comm. Math. Phys. 143 (1992), 501-525. Zbl0745.76001MR1145596
- [7] H. Chan – C. C. Fu – C. S. Lin, Non-topological multivortex solutions to the self-dual Chern-Simons-Higgs equations, Comm. Math. Phys. 231 (2002), 189-221. Zbl1018.58008MR1946331
- [8] S. Chanillo – M. Kiessling, Rotational symmetry of solutions of some nonlinear problems in statistical mechanics and in geometry, Comm. Math. Phys. 160 (1994), 217-238. Zbl0821.35044MR1262195
- [9] S. Y. Chang – P. Yang, Prescribing Gaussian curvature on , Acta Math. 159 (1987), 215-259. Zbl0636.53053MR908146
- [10] C. C. Chen – C. S. Lin, On the symmetry of blowup solutions to a mean field equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001), 271-296. Zbl0995.35004MR1831657
- [11] C. C. Chen – C. S. Lin, Sharp estimates for solutions of multi-bubbles in compact Riemann surfaces, Comm. Pure Appl. Math. 4 (2002), 728-771. Zbl1040.53046MR1885666
- [12] C. C. Chen and C. S. Lin, Topological Degree for a Mean Field Equation on Riemann Surfaces, Comm. Pure Appl. Math. 56 (2003), 1667-1707. Zbl1032.58010MR2001443
- [13] K. S. Chou - Tom Y. H. Wan, Asymptotic radial symmetry for solutions of in a punctured disc, Pacific J. Math. 163 (1994), 269-276. Zbl0794.35049MR1262297
- [14] W. Ding – J. Jost – J. Li – G. Wang, Multiplicity results of two-vortex Chern-Simons-Higgs model on the two-sphere, Comm. Math. Helv. 74 (1999), 118-142. Zbl0913.53032MR1677094
- [15] W. Ding – J. Jost – J. Li – G. Wang, The differential equation of on a compact Riemann surface, Asian J. Math., 1 (1997), 230-248. Zbl0955.58010MR1491984
- [16] W. Ding – J. Jost – J. Li – X. Peng – G. Wang, Self duality equations for Ginzburg-Landau and Seiberg-Witten type functional with 6th order potenliatls, Comm. Math. Phys. 217 (2001), 383-407. Zbl0994.58009MR1821229
- [17] G. Dunne, “Self-dual Chern-Simons Theories”, Lecture Notes in Physics m36, Springer-Verlag, Berlin, 1995. Zbl0834.58001
- [18] J. Hong – Y. Kim – P. Y. Pac, Multivortex solutions of the Abelian Chern Simons theory, Phys. Rev. Letter 64 (1990), 2230-2233. Zbl1014.58500MR1050529
- [19] R. Jackiw – E. J. Weinberg, Selfdual Chern Simons vortices, Phys. Rev. Lett. 64 (1990), 2234-2237. Zbl1050.81595MR1050530
- [20] Y. Y. Li, Harnack type inequality: the method of moving planes, Comm. Math. Phys. 200 (1999), 421-444. Zbl0928.35057MR1673972
- [21] C. S. Lin, Topological degree for mean field equations on , Duke Math. J. 104 (2000), 501-536. Zbl0964.35038MR1781481
- [22] C. S. Lin, Uniqueness of solutions to the mean field equations for the spherical Onsager vortex, Arch. Ration. Mech. Anal. 153 (2000), 153–176. Zbl0968.35045MR1770683
- [23] M. Nolasco, Non-topological -vortex condensates for the self-dual chern-Simons theory, Comm. Pure Appl. Math. 56 (2003), 1752-1780. Zbl1032.58005MR2001445
- [24] M. Nolasco – G. Tarantello, Double vortex condensates in the Chern-Simons-Higgs theory, Calc. Var. Partial Differential Equations 9 (1999), 31-94. Zbl0951.58030MR1710938
- [25] M. Nolasco – G. Tarantello, On a sharp Sobolev-type inequality on two-dimensional compact manifolds, Arch. Ration. Mech. Anal. 145 (1998), 161-195. Zbl0980.46022MR1664542
- [26] J. Prajapat – G. Tarantello, On a class of elliptic problems in : symmetry and uniqueness results, Proc. Roy. Soc. Edinburgh Sect. A 131 (2001), 967-985. Zbl1009.35018MR1855007
- [27] Spruck – Y. Yang, Topological solutions in the self-dual Chern-Simons theory: existence and approximation, Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995), 75-97. Zbl0836.35007MR1320569
- [28] Taubes, Arbitrary -vortex solutions to the first order Ginzburg-Landau equations, Comm. Math. Phys. 72 (1980), 277-292. Zbl0451.35101MR573986
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.