On Stability of Solutions to Equations Describing Incompressible Heat-Conducting Motions Under Navier’s Boundary Conditions

On Stability of Solutions to Equations Describing Incompressible Heat-Conducting Motions Under Navier’s Boundary Conditions

In this paper we prove existence of global strong-weak two-dimensional solutions to the Navier-Stokes and heat equations coupled by the external force dependent on temperature and the heat dissipation, respectively. The existence is proved in a bounded domain with the Navier boundary conditions for...

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Veröffentlicht in:Acta applicandae mathematicae 2017-12, Vol.152 (1), p.147-170
Hauptverfasser: Zadrzyńska, Ewa, Zaja̧czkowski, Wojciech M.
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Boundary conditions
Calculus of Variations and Optimal Control
Optimization
Computational Mathematics and Numerical Analysis
Dirichlet problem
Fluid dynamics
Fluid flow
Heat
Heat transmission
Mathematical analysis
Mathematics
Mathematics and Statistics
Motion stability
Navier-Stokes equations
Partial Differential Equations
Probability Theory and Stochastic Processes
Thermodynamics
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Zusammenfassung:In this paper we prove existence of global strong-weak two-dimensional solutions to the Navier-Stokes and heat equations coupled by the external force dependent on temperature and the heat dissipation, respectively. The existence is proved in a bounded domain with the Navier boundary conditions for velocity and the Dirichlet boundary condition for temperature. Next, we prove existence of 3d global strong solutions via stability.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-017-0116-3