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On the well-posedness of Maxwell-Chern-Simons-Higgs system in the Lorenz gauge
1. | Department of Basic Science, Yancheng Institute of Technology, Yancheng 224051, China |
References:
[1] |
H. Brezis and T. Gallouet, Nonlinear Schrödinger evolution equations, Nonlinear Analysis, Theory, Methods and Applications, 4 (1980), 677-681.
doi: 10.1016/0362-546X(80)90068-1. |
[2] |
N. Bournaveas, Low regularity solutions of the relativistic Chern-Simons-Higgs theory in the Lorentz gauge, Electronic Journal of Differential Equations (2009), 1-10. |
[3] |
D. Chae and M. Chae, The global existence in the Cauchy problem of the Maxwell-Chern- Simons-Higgs system, Journal of Mathematical physics, 43 (2002),5470-5482.
doi: 10.1063/1.1507609. |
[4] |
P. D'Ancona, D. Foschi and S. Selberg, Product estimates for wave-Sobolev spaces in 2+1 and 1+1 dimensions, In Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena, Contemporary Mathematics, vol. 526, Amer. Math. Soc., Providence, RI, 2010, pp. 125-150.
doi: 10.1090/conm/526/10379. |
[5] |
J. Ginibre and G. Velo, The Cauchy problem for coupled Yang-Mills and scalar fields in the temporal gauge, Commun. Math. Phys., 82 (1981/82), 1-28.
doi: 10.1007/BF01206943. |
[6] |
H. Huh, Low regularity solutions of the Chern-Simons-Higgs equations, Nonlinearity, 18 (2005), 2581-2589.
doi: 10.1088/0951-7715/18/6/009. |
[7] |
H. Huh, Local and global solutions of the Chern-Simons-Higgs system, Journal of Functional Analysis, 242 (2007), 526-549.
doi: 10.1016/j.jfa.2006.09.009. |
[8] |
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. |
[9] |
S. Klainerman and M. Machedon, On the Maxwell-Klein-Gordon equation with finite energy, Duke Math. J., 74 (1994), 19-44.
doi: 10.1215/S0012-7094-94-07402-4. |
[10] |
C. Lee, K. Lee and H. Min, Self-dual Maxwell-Chern-Simons solitons, phys. Lett. B, 252 (1990), 79-83.
doi: 10.1016/0370-2693(90)91084-O. |
[11] |
V. Moncrief, Global existence of Maxwell-Klein-Gordon fields in (2+1)-dimensional space-time, Journal of mathematical physics, 21 (1980), 2291-2296.
doi: 10.1063/1.524669. |
[12] |
S. Selberg and A. Tesfahun, Finite-energy global well-posedness of the Maxwell-Klein-Gordon system in Lorenz gauge, Communications in Partial Differential Equations, 35 (2010), 1029-1057.
doi: 10.1080/03605301003717100. |
[13] |
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. |
[14] |
J. Yuan, Local well-posedness of Chern-Simons-Higgs system in the Lorentz gauge, Journal of Mathematical Physics, 52 (2011), 103706, 14 pp.
doi: 10.1063/1.3645365. |
show all references
References:
[1] |
H. Brezis and T. Gallouet, Nonlinear Schrödinger evolution equations, Nonlinear Analysis, Theory, Methods and Applications, 4 (1980), 677-681.
doi: 10.1016/0362-546X(80)90068-1. |
[2] |
N. Bournaveas, Low regularity solutions of the relativistic Chern-Simons-Higgs theory in the Lorentz gauge, Electronic Journal of Differential Equations (2009), 1-10. |
[3] |
D. Chae and M. Chae, The global existence in the Cauchy problem of the Maxwell-Chern- Simons-Higgs system, Journal of Mathematical physics, 43 (2002),5470-5482.
doi: 10.1063/1.1507609. |
[4] |
P. D'Ancona, D. Foschi and S. Selberg, Product estimates for wave-Sobolev spaces in 2+1 and 1+1 dimensions, In Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena, Contemporary Mathematics, vol. 526, Amer. Math. Soc., Providence, RI, 2010, pp. 125-150.
doi: 10.1090/conm/526/10379. |
[5] |
J. Ginibre and G. Velo, The Cauchy problem for coupled Yang-Mills and scalar fields in the temporal gauge, Commun. Math. Phys., 82 (1981/82), 1-28.
doi: 10.1007/BF01206943. |
[6] |
H. Huh, Low regularity solutions of the Chern-Simons-Higgs equations, Nonlinearity, 18 (2005), 2581-2589.
doi: 10.1088/0951-7715/18/6/009. |
[7] |
H. Huh, Local and global solutions of the Chern-Simons-Higgs system, Journal of Functional Analysis, 242 (2007), 526-549.
doi: 10.1016/j.jfa.2006.09.009. |
[8] |
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. |
[9] |
S. Klainerman and M. Machedon, On the Maxwell-Klein-Gordon equation with finite energy, Duke Math. J., 74 (1994), 19-44.
doi: 10.1215/S0012-7094-94-07402-4. |
[10] |
C. Lee, K. Lee and H. Min, Self-dual Maxwell-Chern-Simons solitons, phys. Lett. B, 252 (1990), 79-83.
doi: 10.1016/0370-2693(90)91084-O. |
[11] |
V. Moncrief, Global existence of Maxwell-Klein-Gordon fields in (2+1)-dimensional space-time, Journal of mathematical physics, 21 (1980), 2291-2296.
doi: 10.1063/1.524669. |
[12] |
S. Selberg and A. Tesfahun, Finite-energy global well-posedness of the Maxwell-Klein-Gordon system in Lorenz gauge, Communications in Partial Differential Equations, 35 (2010), 1029-1057.
doi: 10.1080/03605301003717100. |
[13] |
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. |
[14] |
J. Yuan, Local well-posedness of Chern-Simons-Higgs system in the Lorentz gauge, Journal of Mathematical Physics, 52 (2011), 103706, 14 pp.
doi: 10.1063/1.3645365. |
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