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<p>We study the vanishing viscosity of isentropic compressible Navier-Stokes equations with density dependent viscous coefficient in the presence of shock wave. Given a shock wave to the corresponding Euler equations, we can construct a sequence of solutions to one-dimensional compressible isentropic Navier-Stokes equations which converge to the shock wave as the viscosity tends to zero. The proof is given by an elementary energy method.</p>

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Vanishing viscosity of one-dimensional isentropic Navier-Stokes equations with density dependent viscous coefficient

  • 期刊论文

  • 发表日期：

    2025年2月24日

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  • Meiying Cui

摘要

We study the vanishing viscosity of isentropic compressible Navier-Stokes equations with density dependent viscous coefficient in the presence of shock wave. Given a shock wave to the corresponding Euler equations, we can construct a sequence of solutions to one-dimensional compressible isentropic Navier-Stokes equations which converge to the shock wave as the viscosity tends to zero. The proof is given by an elementary energy method.