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Global existence and large time behaviors of the solutions to the full incompressible Navier-Stokes equations with temperature-dependent coefficients

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Abstract We studied an initial boundary value problem for the full incompressible Navier-Stokes equations with viscosity μ and heat conductivity κ depending on temperature by the power law of Chapman-Enskog.… Click to show full abstract

Abstract We studied an initial boundary value problem for the full incompressible Navier-Stokes equations with viscosity μ and heat conductivity κ depending on temperature by the power law of Chapman-Enskog. With this focus, the existence of global-in-time strong solution, under some appropriate smallness assumptions on initial data, has been proved in this paper. Moreover, the large-time behavior and decay rate estimates of the strong solution are obtained.

Keywords: full incompressible; stokes equations; time; incompressible navier; navier stokes; large time

Journal Title: Journal of Differential Equations
Year Published: 2021

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