Abstract
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.
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Yang, J., Ju, Q. & Yang, YF. Asymptotic limits of Navier–Stokes equations with quantum effects. Z. Angew. Math. Phys. 66, 2271–2283 (2015). https://doi.org/10.1007/s00033-015-0554-6
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DOI: https://doi.org/10.1007/s00033-015-0554-6