On the global well-posedness and exponential stability of 3D heat conducting incompressible Navier-Stokes equations with temperature-dependent coefficients and vacuum
This paper focuses on investigating the initial-boundary value problem of incompressible heat conducting Navier-Stokes equations with variable coefficients over bounded domains in $ \mathbb{R}^3 $, where the viscosity coefficient and heat conduction coefficient are powers of temperature. We obtain t...
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| Language: | English |
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AIMS Press
2024-09-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024253 |
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| author | Jianxia He Qingyan Li |
| author_facet | Jianxia He Qingyan Li |
| author_sort | Jianxia He |
| collection | DOAJ |
| description | This paper focuses on investigating the initial-boundary value problem of incompressible heat conducting Navier-Stokes equations with variable coefficients over bounded domains in $ \mathbb{R}^3 $, where the viscosity coefficient and heat conduction coefficient are powers of temperature. We obtain the global well-posedness of a strong solution under the assumption that the initial data and the measure of the initial vacuum region are sufficiently small. It is worth mentioning that the initial density is allowed to contain vacuum, and there are no restrictions on the power index of the temperature-dependent viscosity coefficient and heat conductivity coefficient. At the same time, the exponential decay-in-time results are also obtained. |
| format | Article |
| id | doaj-art-a9aba4237f224ab1a67a3c73484c2bab |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-a9aba4237f224ab1a67a3c73484c2bab2025-01-23T07:52:42ZengAIMS PressElectronic Research Archive2688-15942024-09-013295451547710.3934/era.2024253On the global well-posedness and exponential stability of 3D heat conducting incompressible Navier-Stokes equations with temperature-dependent coefficients and vacuumJianxia He0Qingyan Li1Center for Nonlinear Studies, School of Mathematics, Northwest University, Xi'an 710127, ChinaSchool of Sciences, Chang'an University, Xi'an 710064, ChinaThis paper focuses on investigating the initial-boundary value problem of incompressible heat conducting Navier-Stokes equations with variable coefficients over bounded domains in $ \mathbb{R}^3 $, where the viscosity coefficient and heat conduction coefficient are powers of temperature. We obtain the global well-posedness of a strong solution under the assumption that the initial data and the measure of the initial vacuum region are sufficiently small. It is worth mentioning that the initial density is allowed to contain vacuum, and there are no restrictions on the power index of the temperature-dependent viscosity coefficient and heat conductivity coefficient. At the same time, the exponential decay-in-time results are also obtained.https://www.aimspress.com/article/doi/10.3934/era.2024253navier-stokes equationsdegenerate and temperature-dependent transport coefficientsstrong solutionvacuum |
| spellingShingle | Jianxia He Qingyan Li On the global well-posedness and exponential stability of 3D heat conducting incompressible Navier-Stokes equations with temperature-dependent coefficients and vacuum Electronic Research Archive navier-stokes equations degenerate and temperature-dependent transport coefficients strong solution vacuum |
| title | On the global well-posedness and exponential stability of 3D heat conducting incompressible Navier-Stokes equations with temperature-dependent coefficients and vacuum |
| title_full | On the global well-posedness and exponential stability of 3D heat conducting incompressible Navier-Stokes equations with temperature-dependent coefficients and vacuum |
| title_fullStr | On the global well-posedness and exponential stability of 3D heat conducting incompressible Navier-Stokes equations with temperature-dependent coefficients and vacuum |
| title_full_unstemmed | On the global well-posedness and exponential stability of 3D heat conducting incompressible Navier-Stokes equations with temperature-dependent coefficients and vacuum |
| title_short | On the global well-posedness and exponential stability of 3D heat conducting incompressible Navier-Stokes equations with temperature-dependent coefficients and vacuum |
| title_sort | on the global well posedness and exponential stability of 3d heat conducting incompressible navier stokes equations with temperature dependent coefficients and vacuum |
| topic | navier-stokes equations degenerate and temperature-dependent transport coefficients strong solution vacuum |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024253 |
| work_keys_str_mv | AT jianxiahe ontheglobalwellposednessandexponentialstabilityof3dheatconductingincompressiblenavierstokesequationswithtemperaturedependentcoefficientsandvacuum AT qingyanli ontheglobalwellposednessandexponentialstabilityof3dheatconductingincompressiblenavierstokesequationswithtemperaturedependentcoefficientsandvacuum |