Solutions to the Equations of Viscous Quantum Hydrodynamics in Multiple Dimensions
نویسنده
چکیده
We study the viscous model of quantum hydrodynamics in a bounded domain of space dimension 1, 2, or 3. This model is a mixed order partial differential system with nonlocal and nonlinear terms for the particle density, current density and electric potential. By a viscous regularization approach, we show existence and uniqueness of local in time solutions. 2000 Mathematics Subject Classification: 35B40, 35Q35, 76Y05
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