Blow-Up of Solutions to Quantum Hydrodynamic Models in Bounded Domains

Maria Gualdani
University of Texas at Austin

We show the blow-up in finite time for solutions to the multi-dimensional quantum hydrodynamic model in bounded domains. 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 assumptions on the initial and boundary data the solution blows up after a finite time.

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