## Quasineutral Limit of the Schr\"odinger-Poisson System in Coulomb Gauge

J. Math. Sci. Univ. Tokyo
Vol. 18 (2011), No. 4, Page 465--489.

Lin, Chi-Kun; Wong, Yau-Shu; Wu, Kung-Chien
Quasineutral Limit of the Schr\"odinger-Poisson System in Coulomb Gauge
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Abstract:
The zero Debye length asymptotic of the Schr\"odinger-Poisson system in Coulomb gauge for ill-prepared initial data is studied. We prove that when the scaled Debye length $\la\to 0$, the current density defined by the solution of the Schr\"odinger-Poisson system in the Coulomb gauge converges to the solution of the rotating incompressible Euler equation plus a fast singular oscillating gradient vector field.

Keywords: Schr\"odinger-Poisson system; Coulomb gauge; rotating incompressible Euler equations; quasi-neutral limit.

Mathematics Subject Classification (2010): Primary 35Q40, Secondary 35Q55, 76Y05.