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| OPTIMAL DECAY RATE OF THE COMPRESSIBLE QUANTUM NAVIER-STOKES EQUATIONS |
| Xueke Pu,Boling Guo |
| (Dept. of Math., Chongqing University, Chongqing 401331, PR China;Institute of Applied Physics and Computational Math., P.O. Box 8009, Beijing 100088, PR China) |
| DOI： |
| Abstract: |
| For quantum fluids governed by the compressible quantum Navier-Stokes equations in $\Bbb R^3$ with viscosity and heat conduction, we prove the optimal $L^p-L^q$ decay rates for the classical solutions near constant states. The proof is based on the detailed linearized decay estimates by Fourier analysis of the operators, which is drastically different from the case when quantum effects are absent. |
| Key words: compressible quantum Navier-Stokes equations; optimal decay rates; energy estimates |