玻姆势对宏观自相互作用粒子系统的影响
On the effects of Bohm's potential on a macroscopic system of self-interacting particles
摘要：
本文考虑一个具有附加势（即所谓的玻姆势）的自相互作用粒子的非定常宏观系统。研究了四阶方程组非负整体解的存在性，并指出了与经典模型结果的不同之处。该问题被认为是在一个有界域上的三维空间，受到初始和Neumann边界条件的粒子密度，和Dirichlet边界条件的自相互作用的潜力。此外，初始数据仅被假定为非负的，并满足弱可积性条件。
英文摘要：
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.
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