We prove the existence of a unique, global classical solution of the quantum Vlasov–Poisson problem posed on the phase space ℝ x3 × ℝ v3. The proof is based on a reformulation of the quantum Vlasov–Poisson problem as a system of countably many Schrödinger equations coupled to a Poisson equation for the potential. The Schrödinger‐Poisson problem is first analysed on a bounded domain in ℝ x3 and the solution of the whole‐space problem is then obtained by a limiting procedure in which the domains ‘tend’ to ℝ x3.
|Original language||English (US)|
|Number of pages||27|
|Journal||Mathematical Methods in the Applied Sciences|
|State||Published - 1991|
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