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A note on the Chern-Simons-Dirac equations in the Coulomb gauge
1. | Department of Mathematics, University of Edinburgh, Edinburgh EH9 3JE, United Kingdom |
2. | Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom |
3. | Department of Mathematics, Faculty of Education, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama City 338-8570, Japan |
References:
[1] |
N. Bournaveas, Low regularity solutions of the Chern-Simons-Higgs equations in the Lorentz gauge, Electron. J. Differential Equations, 2009, 10 pp. |
[2] |
N. Bournaveas, T. Candy and S. Machihara, Local and global well-posedness for the Chern-Simons-Dirac system in one dimension, Differential Integral Equations, 25 (2012), 699-718. |
[3] |
S. S. Chern and J. Simons, Characteristic forms and geometric invariants, Ann. of Math. (2), 99 (1974), 48-69.
doi: 10.2307/1971013. |
[4] |
Y. M. Cho, J. W. Kim and D. H. Park, Fermionic vortex solutions in Chern-Simons electrodynamics, Phys. Rev. D (3), 45 (1992), 3802-3806.
doi: 10.1103/PhysRevD.45.3802. |
[5] |
S. Deser, R. Jackiw and S. Templeton, Three-dimensional massive gauge theories, Physical Review Letters, 48 (1982), 975-978.
doi: 10.1103/PhysRevLett.48.975. |
[6] |
H. Huh, Cauchy problem for the fermion field equation coupled with the Chern-Simons gauge, Lett. Math. Phys., 79 (2007), 75-94.
doi: 10.1007/s11005-006-0118-y. |
[7] |
_______, Local and global solutions of the Chern-Simons-Higgs system, J. Funct. Anal., 242 (2007), 526-549.
doi: 10.1016/j.jfa.2006.09.009. |
[8] |
_______, Global solutions and asymptotic behaviors of the Chern-Simons-Dirac equations in $\mathbbR^{1+1}$, J. Math. Anal. Appl., 366 (2010), 706-713.
doi: 10.1016/j.jmaa.2009.12.055. |
[9] |
_______, Towards the Chern-Simons-Higgs equation with finite energy, Discrete Contin. Dyn. Syst., 30 (2011), 1145-1159.
doi: 10.3934/dcds.2011.30.1145. |
[10] |
H. Huh and S.-J. Oh, Low regularity solutions to the Chern-Simons-Dirac and the Chern-Simons-Higgs equations in the Lorenz gauge, preprint, arXiv:1209.3841, (2012). |
[11] |
S. Klainerman and S. Selberg, Bilinear estimates and applications to nonlinear wave equations, Commun. Contemp. Math., 4 (2002), 223-295.
doi: 10.1142/S0219199702000634. |
[12] |
S. Klainerman and D. Tataru, On the optimal local regularity for Yang-Mills equations in $R^{4+1}$, J. Amer. Math. Soc., 12 (1999), 93-116.
doi: 10.1090/S0894-0347-99-00282-9. |
[13] |
H. Lindblad, Counterexamples to local existence for semi-linear wave equations, Amer. J. Math., 118 (1996), 1-16.
doi: 10.1353/ajm.1996.0002. |
[14] |
B. Liu, P. Smith and D. Tataru, Local wellposedness of Chern-Simons-Schrödinger, preprint, arXiv:1212.1476, (2012).
doi: 10.1093/imrn/rnt161. |
[15] |
A. Lopez and E. Fradkin, Fractional quantum Hall effect and Chern-Simons gauge theories, Phys. Rev. B, 44 (1991), 5246-5262.
doi: 10.1103/PhysRevB.44.5246. |
[16] |
S. Selberg and A. Tesfahun, Global well-posedness of the Chern-Simons-Higgs equations with finite energy, Discrete Contin. Dyn. Syst., 33 (2013), 2531-2546.
doi: 10.3934/dcds.2013.33.2531. |
show all references
References:
[1] |
N. Bournaveas, Low regularity solutions of the Chern-Simons-Higgs equations in the Lorentz gauge, Electron. J. Differential Equations, 2009, 10 pp. |
[2] |
N. Bournaveas, T. Candy and S. Machihara, Local and global well-posedness for the Chern-Simons-Dirac system in one dimension, Differential Integral Equations, 25 (2012), 699-718. |
[3] |
S. S. Chern and J. Simons, Characteristic forms and geometric invariants, Ann. of Math. (2), 99 (1974), 48-69.
doi: 10.2307/1971013. |
[4] |
Y. M. Cho, J. W. Kim and D. H. Park, Fermionic vortex solutions in Chern-Simons electrodynamics, Phys. Rev. D (3), 45 (1992), 3802-3806.
doi: 10.1103/PhysRevD.45.3802. |
[5] |
S. Deser, R. Jackiw and S. Templeton, Three-dimensional massive gauge theories, Physical Review Letters, 48 (1982), 975-978.
doi: 10.1103/PhysRevLett.48.975. |
[6] |
H. Huh, Cauchy problem for the fermion field equation coupled with the Chern-Simons gauge, Lett. Math. Phys., 79 (2007), 75-94.
doi: 10.1007/s11005-006-0118-y. |
[7] |
_______, Local and global solutions of the Chern-Simons-Higgs system, J. Funct. Anal., 242 (2007), 526-549.
doi: 10.1016/j.jfa.2006.09.009. |
[8] |
_______, Global solutions and asymptotic behaviors of the Chern-Simons-Dirac equations in $\mathbbR^{1+1}$, J. Math. Anal. Appl., 366 (2010), 706-713.
doi: 10.1016/j.jmaa.2009.12.055. |
[9] |
_______, Towards the Chern-Simons-Higgs equation with finite energy, Discrete Contin. Dyn. Syst., 30 (2011), 1145-1159.
doi: 10.3934/dcds.2011.30.1145. |
[10] |
H. Huh and S.-J. Oh, Low regularity solutions to the Chern-Simons-Dirac and the Chern-Simons-Higgs equations in the Lorenz gauge, preprint, arXiv:1209.3841, (2012). |
[11] |
S. Klainerman and S. Selberg, Bilinear estimates and applications to nonlinear wave equations, Commun. Contemp. Math., 4 (2002), 223-295.
doi: 10.1142/S0219199702000634. |
[12] |
S. Klainerman and D. Tataru, On the optimal local regularity for Yang-Mills equations in $R^{4+1}$, J. Amer. Math. Soc., 12 (1999), 93-116.
doi: 10.1090/S0894-0347-99-00282-9. |
[13] |
H. Lindblad, Counterexamples to local existence for semi-linear wave equations, Amer. J. Math., 118 (1996), 1-16.
doi: 10.1353/ajm.1996.0002. |
[14] |
B. Liu, P. Smith and D. Tataru, Local wellposedness of Chern-Simons-Schrödinger, preprint, arXiv:1212.1476, (2012).
doi: 10.1093/imrn/rnt161. |
[15] |
A. Lopez and E. Fradkin, Fractional quantum Hall effect and Chern-Simons gauge theories, Phys. Rev. B, 44 (1991), 5246-5262.
doi: 10.1103/PhysRevB.44.5246. |
[16] |
S. Selberg and A. Tesfahun, Global well-posedness of the Chern-Simons-Higgs equations with finite energy, Discrete Contin. Dyn. Syst., 33 (2013), 2531-2546.
doi: 10.3934/dcds.2013.33.2531. |
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