On the Cauchy problem for Wigner–Poisson–BGK equation in the Wiener algebra

In this paper, we prove the existence and uniqueness of the local mild solution to the Cauchy problem of the n‐dimensional (n≥3) Wigner–Poisson–BGK equation in the space of some integrable functions whose inverse Fourier transform are integrable. The main difficulties in establishing mild solution are to derive the boundedness and locally Lipschitz properties of the appropriate nonlinear terms in the Wiener algebra. Copyright © 2015 John Wiley & Sons, Ltd.