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

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

2007-04-24

arxiv.org/abs/0704.3110v1

Physics

Mathematical Physics

14 pages

Scientific paper

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.

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