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

TL;DR

This paper investigates the impact of Bohm's potential on a macroscopic system of self-interacting particles, focusing on the existence of global solutions and comparing with classical models.

Contribution

It establishes the existence of non-negative global solutions for a 4th-order system with Bohm's potential, extending classical results to include quantum effects.

Findings

Proved existence of solutions under weak initial conditions

Identified differences from classical particle models

Analyzed boundary conditions' effects on solutions

Abstract

We consider an instationary macroscopic system of self-interacting particles with an additional potential, the so called Bohm's potential. We study the existence of non-negative global solutions to the (4-th order) system of equations and allude the differences to results obtained for classical models. The problem is considered on a bounded domain up to three space dimension, subject to initial and Neumann boundary condition for the particle density, and Dirichlet boundary condition for the self-interacting potential. Moreover, the initial datum is only assumed to be non-negative and to satisfy a weak integrability condition.