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Uniform Regularity for the Time-Dependent Ginzburg-Landau-Maxwell Equations

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New Trends in Analysis and Interdisciplinary Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

We study global weak solutions to the 3D time-dependent Ginzburg-Landau-Maxwell equations with the Coulomb gauge. We obtain uniform bounds of solutions with respect to the dielectric constant ε > 0. Consequently, the existence of global weak solutions to the Ginzburg-Landau equations follows by a compactness argument.

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Acknowledgements

J. Fan is partially supported by NSFC (No. 11171154). This work was supported by JSPS KAKENHI Grant Numbers 26247014, 25610027.

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Authors and Affiliations

  1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, People’s Republic of China

    Jishan Fan

  2. Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan

    Tohru Ozawa

Authors
  1. Jishan Fan
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  2. Tohru Ozawa
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Corresponding author

Correspondence to Jishan Fan .

Editor information

Editors and Affiliations

  1. Faculty of Information Technology, Macau University of Science and Technology, Taipa, Macao

    Pei Dang

  2. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Min Ku

  3. Faculty of Science and Technology, Department of Mathematics, University of Macau, Taipa, Macao

    Tao Qian

  4. Department of Mathematics, University of Torino, Torino, Italy

    Luigi G. Rodino

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Fan, J., Ozawa, T. (2017). Uniform Regularity for the Time-Dependent Ginzburg-Landau-Maxwell Equations. In: Dang, P., Ku, M., Qian, T., Rodino, L. (eds) New Trends in Analysis and Interdisciplinary Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-48812-7_38

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