Zero-viscosity-capillarity limit for the contact discontinuity for the 1-D full compressible Navier-Stokes-Korteweg equations
In this article, we study the zero-viscosity-capillarity limit problem for the one-dimensional full compressible Navier-Stokes-Korteweg equations. This equation models compressible viscous fluids with internal capillarity and heat conductivity. We prove that if the solution of the inviscid Euler eq...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2025-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/74/abstr.html |
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| Summary: | In this article, we study the zero-viscosity-capillarity limit problem for the one-dimensional
full compressible Navier-Stokes-Korteweg equations. This equation models
compressible viscous fluids with internal capillarity and heat
conductivity. We prove that if the solution of the inviscid Euler
equations is piecewise constants with a contact discontinuity, then
there exist smooth solutions to the one-dimensional full
compressible Navier-Stokes-Korteweg system which converge to the
inviscid solution away from the contact discontinuity.
It converges a rate of $\epsilon^{1/4}$ as the the viscosity $\mu=\epsilon$,
heat-conductivity coefficient $\alpha=\nu\epsilon$ and the
capillarity $\kappa=\lambda\epsilon^2$ and $\epsilon$ tends to
zero. The proof is completed using the energy method and the scaling
technique. |
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| ISSN: | 1072-6691 |