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<p>We investigate the existence and the zero viscosity limit of steady compressible shear flows with Navier-slip boundary conditions in the absence of any external force in a two-dimensional domain Ω = (0,<i>L</i>) × (0, 2). More precisely, under the assumption that the Mach number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\eta&lt;\varepsilon^{\frac{1}{2}+}\)</EquationSource> </InlineEquation>and <i>L</i> ≪ 1, we prove the existence of smooth solutions to steady compressible Naiver-Stokes equations near plane Poiseuille-Couette flows as well as the convergence of the solutions obtained above to the solutions of steady incompressible Euler equations when the viscous <i>ε</i> tends to zero.</p>

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Zero viscosity limit of steady compressible shear flows with Navier-slip boundary conditions

  • 期刊论文

  • 发表日期：

    2025年9月22日

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  • Wenbin Li,
  • Chunhui Zhou

摘要

We investigate the existence and the zero viscosity limit of steady compressible shear flows with Navier-slip boundary conditions in the absence of any external force in a two-dimensional domain Ω = (0,L) × (0, 2). More precisely, under the assumption that the Mach number \(\eta<\varepsilon^{\frac{1}{2}+}\) and L ≪ 1, we prove the existence of smooth solutions to steady compressible Naiver-Stokes equations near plane Poiseuille-Couette flows as well as the convergence of the solutions obtained above to the solutions of steady incompressible Euler equations when the viscous ε tends to zero.