This paper is concerned with the Wigner(–Poisson)–Fokker–Planck equation with coupling to the confining potential which is a singular perturbation of the harmonic oscillator potential. In this work, we study the… Click to show full abstract
This paper is concerned with the Wigner(–Poisson)–Fokker–Planck equation with coupling to the confining potential which is a singular perturbation of the harmonic oscillator potential. In this work, we study the global (local) existence and uniqueness of these solutions on different weighted- space, respectively. The main difficulties for establishing global (local) mild solution are to derive a-priori estimates on the appropriate potential terms and obtain dissipativity of the quantum Fokker–Planck operator. The proofs are based on semigroup theory and -weighted Hardy’s inequality.
               
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