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Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 3
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Research Article

Global strong solutions to the Cauchy problem of the 3D heat-conducting fluids

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Pages 600-617 | Received 09 Nov 2022, Accepted 30 Mar 2023, Published online: 16 Apr 2023
 

Abstract

In this paper, we study the global strong solutions to the three-dimensional (3D) heat-conducting incompressible Navier–Stokes equations with density-temperature-dependent viscosity and heat-conducting coefficients in R3. By using the t-weighted a priori estimates, we prove the global existence and exponential decay-in-time rates of strong solutions to the Cauchy problem when the L3/2-norm of the initial density is suitably small. It should be noted that the velocity and absolute temperature can be large initially, and the initial density contains vacuum case.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by Xinjiang University of Finance and Economics Research Fund Project [grant number 2022XYB006].

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