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Global Energy Solution to the Schrödinger Equation Coupled with the Chern-Simons Gauge and Neutral Field

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  • Hyungjin Huh
  • Bora Moon

Abstract

We study the Cauchy problem of the Chern-Simons-Schrödinger equations with a neutral field, under the Coulomb gauge condition, in energy space . We prove the uniqueness of a solution by using the Gagliardo-Nirenberg inequality with the specific constant. To obtain a global solution, we show the conservation of total energy and find a bound for the nondefinite term.

Suggested Citation

  • Hyungjin Huh & Bora Moon, 2018. "Global Energy Solution to the Schrödinger Equation Coupled with the Chern-Simons Gauge and Neutral Field," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-8, June.
    • Handle: RePEc:hin:jnlamp:3962062
    DOI: 10.1155/2018/3962062
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