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The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case. (English) Zbl 0742.35078
Summary: We prove the global existence of a unique classical solution of the two- dimensional Wigner-Poisson problem by a reformulation as a system of countably many Schrödinger equations coupled to a Poisson equation. The charge neutrality of the system implies the boundedness of the electrostatic potential in two dimensions, which is an important ingredient for the proof.

35S10 Initial value problems for PDEs with pseudodifferential operators
35K55 Nonlinear parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
47D03 Groups and semigroups of linear operators
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
Full Text: DOI
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