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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2025-07-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/74/abstr.html |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849341236863827968 |
|---|---|
| author | Jiaxue Chen Yeping Li Rong Yin |
| author_facet | Jiaxue Chen Yeping Li Rong Yin |
| author_sort | Jiaxue Chen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-debaa694289643a8a9c4f53c64eb24b2 |
| institution | Kabale University |
| issn | 1072-6691 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj-art-debaa694289643a8a9c4f53c64eb24b22025-08-20T03:43:40ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912025-07-01202574,118Zero-viscosity-capillarity limit for the contact discontinuity for the 1-D full compressible Navier-Stokes-Korteweg equationsJiaxue Chen0Yeping Li1Rong Yin2 Nantong Univ., Nantong, China Nantong Univ., Nantong, China Nantong Univ., Nantong, China 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.http://ejde.math.txstate.edu/Volumes/2025/74/abstr.htmlfull compressible navier-stokes-korteweg equationcompressible euler systemzero-viscosity-capillarity limitcontact discontinuity |
| spellingShingle | Jiaxue Chen Yeping Li Rong Yin Zero-viscosity-capillarity limit for the contact discontinuity for the 1-D full compressible Navier-Stokes-Korteweg equations Electronic Journal of Differential Equations full compressible navier-stokes-korteweg equation compressible euler system zero-viscosity-capillarity limit contact discontinuity |
| title | Zero-viscosity-capillarity limit for the contact discontinuity for the 1-D full compressible Navier-Stokes-Korteweg equations |
| title_full | Zero-viscosity-capillarity limit for the contact discontinuity for the 1-D full compressible Navier-Stokes-Korteweg equations |
| title_fullStr | Zero-viscosity-capillarity limit for the contact discontinuity for the 1-D full compressible Navier-Stokes-Korteweg equations |
| title_full_unstemmed | Zero-viscosity-capillarity limit for the contact discontinuity for the 1-D full compressible Navier-Stokes-Korteweg equations |
| title_short | Zero-viscosity-capillarity limit for the contact discontinuity for the 1-D full compressible Navier-Stokes-Korteweg equations |
| title_sort | zero viscosity capillarity limit for the contact discontinuity for the 1 d full compressible navier stokes korteweg equations |
| topic | full compressible navier-stokes-korteweg equation compressible euler system zero-viscosity-capillarity limit contact discontinuity |
| url | http://ejde.math.txstate.edu/Volumes/2025/74/abstr.html |
| work_keys_str_mv | AT jiaxuechen zeroviscositycapillaritylimitforthecontactdiscontinuityforthe1dfullcompressiblenavierstokeskortewegequations AT yepingli zeroviscositycapillaritylimitforthecontactdiscontinuityforthe1dfullcompressiblenavierstokeskortewegequations AT rongyin zeroviscositycapillaritylimitforthecontactdiscontinuityforthe1dfullcompressiblenavierstokeskortewegequations |