Jiaxue Chen, Yeping Li, Rong Yin
Abstract:
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.
Submitted May 19, 2025. Published July 16, 2025.
Math Subject Classifications: 76W05, 35B40.
Key Words: Full compressible Navier-Stokes-Korteweg equation; compressible Euler system;
zero-viscosity-capillarity limit; contact discontinuity.
DOI: 10.58997/ejde.2025.74
Show me the PDF file (385 KB), TEX file for this article.
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Jiaxue Chen School of Mathematics and statistics Nantong University Nantong 226019, China email: jxchen2025@163.com |
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Yeping Li School of Mathematics and statistics Nantong University Nantong 226019, China email: ypleemei@aliyun.com |
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Rong Yin School of Mathematics and statistics Nantong University Nantong 226019, China email: yin.r@ntu.edu.cn |
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