| Abstract: |
| In this paper we study the incompressible limit of the degenerate quantum
compressible Navier-Stokes equations in a periodic domain $\mathbb{T}^3$ and the whole space $\mathbb{R}^3$ with general initial data.
In the periodic case, by applying the refined related entropy method and carrying out the detailed analysis on the oscillations of velocity, we
prove rigorously that the gradient part of the weak solutions (velocity) of the degenerate quantum compressible Navier-Stokes equations
converge to the strong solution of the incompressible Navier-Stokes equations.
While for the whole space case, thanks to the Strichartz's estimates of linear wave equations, we can obtain the convergence of the weak solutions of the degenerate quantum compressible Navier-Stokes equations to the strong solution of the incompressible Navier-Stokes/Euler equations with a linear damping term. Moreover, the convergence rates are also given. |
|