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Small Data Global Existence and Decay for Relativistic Chern–Simons Equations

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Abstract

We establish a general small data global existence and decay theorem for Chern–Simons theories with a general gauge group, coupled with a massive relativistic field of spin 0 or 1/2. Our result applies to a wide range of relativistic Chern–Simons theories considered in the literature, including the abelian/non-abelian self-dual Chern–Simons–Higgs equation and the Chern–Simons–Dirac equation. A key idea is to develop and employ a gauge invariant vector field method for relativistic Chern–Simons theories, which allows us to avoid the long-range effect of charge.

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Authors and Affiliations

  1. Department of Mathematics, Hankyung University, Anseong-si, Gyeonggi-do, Korea

    Myeongju Chae

  2. Korea Institute for Advanced Study, Seoul, Korea

    Sung-Jin Oh

Authors
  1. Myeongju Chae
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  2. Sung-Jin Oh
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Correspondence to Sung-Jin Oh.

Additional information

Communicated by James A. Isenberg.

The authors thank Hyungjin Huh for helpful discussions. M. Chae was partially supported by NRF-2015R1C1A2A01054919. A major part of this work was done, while S.-J. Oh was supported by the Miller Research Fellowship from the Miller Institute at UC Berkeley.

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Chae, M., Oh, SJ. Small Data Global Existence and Decay for Relativistic Chern–Simons Equations. Ann. Henri Poincaré 18, 2123–2198 (2017). https://doi.org/10.1007/s00023-016-0547-9

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