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April  2016, 36(4): 2193-2204. doi: 10.3934/dcds.2016.36.2193

Local solutions with infinite energy of the Maxwell-Chern-Simons-Higgs system in Lorenz gauge

Hartmut Pecher 1,

1. 

Fachbereich Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany

Received  November 2014 Revised  July 2015 Published  September 2015

We consider the Maxwell-Chern-Simons-Higgs system in Lorenz gauge and use a null condition to show local well-psoedness for low regularity data. This improves a recent result of J. Yuan.
Keywords: Maxwell-Chern-Simons-Higgs, Lorenz gauge., local well-posedness.
Mathematics Subject Classification: 35Q40, 35L7.
Citation: Hartmut Pecher. Local solutions with infinite energy of the Maxwell-Chern-Simons-Higgs system in Lorenz gauge. Discrete & Continuous Dynamical Systems, 2016, 36 (4) : 2193-2204. doi: 10.3934/dcds.2016.36.2193
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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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