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<p>In this paper we study the combined inviscid and semi-classical limits of the quantum Navier–Stokes equations in a periodic domain <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {T}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">T</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>. Under some suitable assumptions, it is rigorously proved that the finite energy weak solutions of the quantum Navier–Stokes equations converge to the strong solution of the classical compressible Euler equations when the viscosity coefficient and the Planck constant go to zero simultaneously. Furthermore, the convergence rates are also obtained.</p>

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Convergence of the Quantum Navier–Stokes Equations to the Compressible Euler Equations

  • 期刊论文

  • 发表日期：

    2025年11月23日

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  • Xiujuang Li,
  • Xiuhui Yang

摘要

In this paper we study the combined inviscid and semi-classical limits of the quantum Navier–Stokes equations in a periodic domain \(\mathbb {T}^3\) T 3 . Under some suitable assumptions, it is rigorously proved that the finite energy weak solutions of the quantum Navier–Stokes equations converge to the strong solution of the classical compressible Euler equations when the viscosity coefficient and the Planck constant go to zero simultaneously. Furthermore, the convergence rates are also obtained.