Large-time behavior of cylindrically symmetric Navier-Stokes equations with temperature-dependent viscosity and heat conductivity

Dandan Song; Xiaokui Zhao; Dandan Song; Xiaokui Zhao

doi:10.3934/cam.2024028

Communications in Analysis and Mechanics

2024, Volume 16, Issue 3: 599-632. doi: 10.3934/cam.2024028

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Research article

Large-time behavior of cylindrically symmetric Navier-Stokes equations with temperature-dependent viscosity and heat conductivity

Dandan Song ¹,
Xiaokui Zhao ^{2
,
,}

1.
School of Mathematics and Statistics, Guizhou University, Guizhou 550025, China
2.
School of Mathematics and Information Science, Henan Polytechnic University, Henan 454000, China

Received: 27 November 2023 Revised: 09 January 2024 Accepted: 17 July 2024 Published: 21 August 2024
35Q35, 76N10

In this study, the initial-boundary value problem for cylindrically symmetric Navier-Stokes equations was considered with temperature-dependent viscosity and heat conductivity. Firstly, we established the existence and uniqueness of a strong solution when the viscosity and heat conductivity were both power functions of temperature. Moreover, the large-time behavior of the strong solution was obtained with large initial data, since all of the estimates in this paper were independent of time. It is worth noting that we identified the relationship between the initial data and the power of the temperature in the viscosity for the first time.
- cylindrically symmetric Navier-Stokes equations,
- existence,
- uniqueness,
- large-time behavior
Citation: Dandan Song, Xiaokui Zhao. Large-time behavior of cylindrically symmetric Navier-Stokes equations with temperature-dependent viscosity and heat conductivity[J]. Communications in Analysis and Mechanics, 2024, 16(3): 599-632. doi: 10.3934/cam.2024028

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Abstract

In this study, the initial-boundary value problem for cylindrically symmetric Navier-Stokes equations was considered with temperature-dependent viscosity and heat conductivity. Firstly, we established the existence and uniqueness of a strong solution when the viscosity and heat conductivity were both power functions of temperature. Moreover, the large-time behavior of the strong solution was obtained with large initial data, since all of the estimates in this paper were independent of time. It is worth noting that we identified the relationship between the initial data and the power of the temperature in the viscosity for the first time.

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