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Well-posedness and blow-up scenario for a new integrable four-component system with peakon solutions
Local solutions with infinite energy of the Maxwell-Chern-Simons-Higgs system in Lorenz gauge
| 1. | Fachbereich Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany |
References:
| [1] |
P. d'Ancona, D. Foschi and S. Selberg, Product estimates for wave-Sobolev spaces in 2+1 and 1+1 dimensions, Contemporary Math., 526 (2010), 125-150.
doi: 10.1090/conm/526/10379. |
| [2] |
D. Chae and M. Chae, The global existence in the Cauchy problem of the Maxwell-Chern-Simons-Higgs system, J. Math. Phys., 43 (2002), 5470-5482.
doi: 10.1063/1.1507609. |
| [3] |
C. Lee, K. Lee and H. Min, Self-dual Maxwell-Chern-Simons solitons, Phys. Letters B, 252 (1990), 79-83.
doi: 10.1016/0370-2693(90)91084-O. |
| [4] |
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. |
| [5] |
S. Selberg and A. Tesfahun, Finite energy global well-posedness of the Maxwell-Klein-Gordon system in Lorenz gauge, Comm. PDE, 35 (2010), 1029-1057.
doi: 10.1080/03605301003717100. |
| [6] |
S. Selberg and A. Tesfahun, Global well-posedness of the Chern-Simons-Higgs equations with finite energy, Discrete Cont. Dyn. Syst., 33 (2013), 2531-2546.
doi: 10.3934/dcds.2013.33.2531. |
| [7] |
J. Yuan, On the well-posedness of Maxwell-Chern-Simons-Higgs system in the Lorenz gauge, Discrete Cont. Dyn. Syst., 34 (2014), 2389-2403.
doi: 10.3934/dcds.2014.34.2389. |
show all references
References:
| [1] |
P. d'Ancona, D. Foschi and S. Selberg, Product estimates for wave-Sobolev spaces in 2+1 and 1+1 dimensions, Contemporary Math., 526 (2010), 125-150.
doi: 10.1090/conm/526/10379. |
| [2] |
D. Chae and M. Chae, The global existence in the Cauchy problem of the Maxwell-Chern-Simons-Higgs system, J. Math. Phys., 43 (2002), 5470-5482.
doi: 10.1063/1.1507609. |
| [3] |
C. Lee, K. Lee and H. Min, Self-dual Maxwell-Chern-Simons solitons, Phys. Letters B, 252 (1990), 79-83.
doi: 10.1016/0370-2693(90)91084-O. |
| [4] |
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. |
| [5] |
S. Selberg and A. Tesfahun, Finite energy global well-posedness of the Maxwell-Klein-Gordon system in Lorenz gauge, Comm. PDE, 35 (2010), 1029-1057.
doi: 10.1080/03605301003717100. |
| [6] |
S. Selberg and A. Tesfahun, Global well-posedness of the Chern-Simons-Higgs equations with finite energy, Discrete Cont. Dyn. Syst., 33 (2013), 2531-2546.
doi: 10.3934/dcds.2013.33.2531. |
| [7] |
J. Yuan, On the well-posedness of Maxwell-Chern-Simons-Higgs system in the Lorenz gauge, Discrete Cont. Dyn. Syst., 34 (2014), 2389-2403.
doi: 10.3934/dcds.2014.34.2389. |
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