Global existence and large time behavior of strong solutions for 3D nonhomogeneous heat conducting Navier–Stokes equations

We are concerned with an initial boundary value problem of nonhomogeneous heat conducting Navier–Stokes equations on a bounded simply connected smooth domain Ω⊆R3, with the Navier-slip boundary condition for velocity and Neumann boundary condition for temperature. We prove that there exists a unique...

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Bibliographic Details
Published in:Journal of mathematical physics 2020-11, Vol.61 (11)
Main Author: Zhong, Xin
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Decay rate
Fluid dynamics
Fluid flow
Heat transfer
Heat transmission
Mathematical analysis
Navier-Stokes equations
Physics
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Summary:We are concerned with an initial boundary value problem of nonhomogeneous heat conducting Navier–Stokes equations on a bounded simply connected smooth domain Ω⊆R3, with the Navier-slip boundary condition for velocity and Neumann boundary condition for temperature. We prove that there exists a unique global strong solution, provided that ‖ρ0u0‖L22‖curlu0‖L22 is suitably small. Moreover, we also obtain the large time decay rates of the solution. Our result improves previous works on this topic.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0012871