Asymptotic limits of Navier-Stokes equations with quantum effects

作者：Yang, Jianwei^*; Ju, Qiangchang; Yang, Yong-Fu

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2015, 66(5): 2271-2283.

DOI：10.1007/s00033-015-0554-6

• Incompressible limit
• Semiclassical limit
• Relative entropy method
• Quantum Navier-Stokes equations
• Incompressible Navier-Stokes equations

This paper is concerned with the combined incompressible limit and semiclassical limit of the weak solutions to the barotropic quantum Navier-Stokes equations of compressible flows. By using the relative entropy method, we show that for well-prepared initial data, the weak solutions of the compressible quantum Navier-Stokes model converge to the strong solution of the incompressible Navier-Stokes equations as long as the latter exists. Furthermore, the convergence rates are also obtained.

• 出版日期2015-10
• 单位北京应用物理与计算数学研究所; 河海大学