On the effects of the Bohm potential on a macroscopic system of self-interacting particles

Abstract

We consider a nonstationary macroscopic system of self-interacting particles with an additional potential, the so called Bohm potential. We study the existence of nonnegative global solutions to the system of equations and allude to the differences to results obtained for classical models. The problem is considered on a bounded domain up to three spatial dimensions, subject to initial and Neumann boundary conditions for the particle density, and the Dirichlet boundary condition for the self-interacting potential. Moreover, the initial datum is only assumed to be nonnegative and to satisfy a weak integrability condition.