A Kato-type criterion for the inviscid limit of the nonhomogeneous NS equations with no-slip boundary condition
The objective of this paper is to examine the vanishing viscosity limit of the nonhomogeneous incompressible NS systerm, subject to the no-slip boundary condition. By adopting Kato's approach of constructing an artificial boundary layer [1], within a smooth and bounded domain designated as $ \O...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | Communications in Analysis and Mechanics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2024039 |
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| author | Shuai Xi |
| author_facet | Shuai Xi |
| author_sort | Shuai Xi |
| collection | DOAJ |
| description | The objective of this paper is to examine the vanishing viscosity limit of the nonhomogeneous incompressible NS systerm, subject to the no-slip boundary condition. By adopting Kato's approach of constructing an artificial boundary layer [1], within a smooth and bounded domain designated as $ \Omega\subseteq\mathbb{R}^{2} $, we derive a sufficient condition for the convergence to occur uniformly in time within the energy space $ L^{2}(\Omega) $. |
| format | Article |
| id | doaj-art-f2517352ba3e4a82808f61329953a0f4 |
| institution | Kabale University |
| issn | 2836-3310 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Communications in Analysis and Mechanics |
| spelling | doaj-art-f2517352ba3e4a82808f61329953a0f42025-01-23T07:55:55ZengAIMS PressCommunications in Analysis and Mechanics2836-33102024-12-0116489690910.3934/cam.2024039A Kato-type criterion for the inviscid limit of the nonhomogeneous NS equations with no-slip boundary conditionShuai Xi0School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, P.R. ChinaThe objective of this paper is to examine the vanishing viscosity limit of the nonhomogeneous incompressible NS systerm, subject to the no-slip boundary condition. By adopting Kato's approach of constructing an artificial boundary layer [1], within a smooth and bounded domain designated as $ \Omega\subseteq\mathbb{R}^{2} $, we derive a sufficient condition for the convergence to occur uniformly in time within the energy space $ L^{2}(\Omega) $.https://www.aimspress.com/article/doi/10.3934/cam.2024039nonhomogeneous ns systemthe vanishing viscosity limitno-slip boundary condition |
| spellingShingle | Shuai Xi A Kato-type criterion for the inviscid limit of the nonhomogeneous NS equations with no-slip boundary condition Communications in Analysis and Mechanics nonhomogeneous ns system the vanishing viscosity limit no-slip boundary condition |
| title | A Kato-type criterion for the inviscid limit of the nonhomogeneous NS equations with no-slip boundary condition |
| title_full | A Kato-type criterion for the inviscid limit of the nonhomogeneous NS equations with no-slip boundary condition |
| title_fullStr | A Kato-type criterion for the inviscid limit of the nonhomogeneous NS equations with no-slip boundary condition |
| title_full_unstemmed | A Kato-type criterion for the inviscid limit of the nonhomogeneous NS equations with no-slip boundary condition |
| title_short | A Kato-type criterion for the inviscid limit of the nonhomogeneous NS equations with no-slip boundary condition |
| title_sort | kato type criterion for the inviscid limit of the nonhomogeneous ns equations with no slip boundary condition |
| topic | nonhomogeneous ns system the vanishing viscosity limit no-slip boundary condition |
| url | https://www.aimspress.com/article/doi/10.3934/cam.2024039 |
| work_keys_str_mv | AT shuaixi akatotypecriterionfortheinviscidlimitofthenonhomogeneousnsequationswithnoslipboundarycondition AT shuaixi katotypecriterionfortheinviscidlimitofthenonhomogeneousnsequationswithnoslipboundarycondition |