On well-posedness of quantum fluid systems in the class of dissipative solutions. (English) Zbl 1529.35326
Summary: The main objects of the present work are the quantum Navier-Stokes and quantum Euler systems; for the first one, in particular, we will consider constant viscosity coefficients. We deal with the concept of dissipative solutions, for which we will first prove the weak-strong uniqueness principle, and afterward, we will show the global existence for any finite energy initial data. Finally, we will prove that both systems admit a semiflow selection in the class of dissipative solutions.
MSC:
| 35Q30 | Navier-Stokes equations |
| 35Q31 | Euler equations |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |
| 82D50 | Statistical mechanics of superfluids |
| 82C10 | Quantum dynamics and nonequilibrium statistical mechanics (general) |
| 82D37 | Statistical mechanics of semiconductors |
| 35D30 | Weak solutions to PDEs |
| 35G35 | Systems of linear higher-order PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 81V70 | Many-body theory; quantum Hall effect |
| 81Q65 | Alternative quantum mechanics (including hidden variables, etc.) |
| 81P15 | Quantum measurement theory, state operations, state preparations |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
Keywords:
quantum fluid systems; dissipative solutions; weak-strong uniqueness; existence; semiflow selectionReferences:
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