Abstract: | 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. |