Small data global existence and decay for relativistic Chern-Simons equations

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.

64 pages, 1 figure

References in corpus (7)

• Non-Abelian Chern-Simons vortices with generic gauge groups
• Fractional and semi-local non-Abelian Chern-Simons vortices
• Global wellposedness of the equivariant Chern-Simons-Schrödinger equation
• Finite energy global well-posedness of the Chern-Simons-Higgs equations in the Coulomb gauge
• Low regularity solutions to the Chern-Simons-Dirac and the Chern-Simons-Higgs equations in the Lorenz gauge
• Low regularity local well-posedness for the Chern-Simons-Higgs system in temporal gauge
• A remark on low regularity solutions of the Chern-Simons-Dirac system