Abstract
We investigate the viscous model of quantum hydrodynamics in one and higher space dimensions. Exploiting the entropy dissipation method, we prove the exponential decay to the thermal equilibrium state in one, two, and three dimensions, provided that the domain is a box. Further, we show the local in time existence of a solution in the one-dimensional case; and in the case of higher dimensions under the assumption of periodic boundary conditions. Finally, we prove the global existence in a one-dimensional setting under additional assumptions.
| Original language | English |
|---|---|
| Pages (from-to) | 1065-1093 |
| Number of pages | 29 |
| Journal | Mathematical Models and Methods in Applied Sciences |
| Volume | 17 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - Jul 2007 |
Keywords
- quantum hydrodynamics
- exponential decay
- entropy dissipation method
- local and global existence of solutions
- EXPONENTIAL DECAY
- EQUATIONS
- SYSTEMS