标题： 关于有界域上量子流体动力学模型解的爆破 显示英文标题

标题： On the blowing up of solutions to quantum hydrodynamic models on bounded domains

摘要： 对于有界域中多维量子流体动力学模型的初始-边界值问题解在有限时间内爆破进行了证明。该模型由质量守恒方程和等价于修正了动量平衡中的三阶色散项的可压缩欧拉方程的动量平衡方程组成。证明基于通过辅助函数构造的新可观测量的能量泛函的先验估计，并且在适当的边界条件和初始数据假设下，显示解在有限时间后爆破。 显示英文摘要

摘要： The blow-up in finite time for the solutions to the initial-boundary value problem associated to the multi-dimensional quantum hydrodynamic model in a bounded domain is proved. The model consists on conservation of mass equation and a momentum balance equation equivalent to a compressible Euler equations corrected by a dispersion term of the third order in the momentum balance. The proof is based on a-priori estimates for the energy functional for a new observable constructed with an auxiliary function, and it is shown that, under suitable boundary conditions and assumptions on the initial data, the solution blows up after a finite time.