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

الملخص EN

We study the Cauchy problem of the Chern-Simons-Schrödinger equations with a neutral field, under the Coulomb gauge condition, in energy space H1(R2).

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.