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7. The Steady Boussinesq System

  • 2021
  • OriginalPaper
  • Chapter
Published in:
Authors
Tujin Kim
Daomin Cao
Published in
Equations of Motion for Incompressible Viscous Fluids
Publisher
Springer International Publishing

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Abstract

The chapter delves into the steady Boussinesq system under mixed boundary conditions, addressing both static and total pressure scenarios. It introduces variational formulations consisting of a variational inequality for velocity and a variational equation for temperature, which are shown to be equivalent to the original PDE problems for smooth solutions. The existence of solutions is rigorously proven, with unique solutions guaranteed under certain conditions. The chapter also discusses auxiliary problems and their solutions, providing a thorough examination of the system's behavior under various boundary conditions.
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previous chapter The Non-steady Navier-Stokes System with Friction Boundary Conditions
next chapter The Non-steady Boussinesq System
Title
The Steady Boussinesq System
Authors
Tujin Kim
Daomin Cao
Copyright Year
2021
Book
Equations of Motion for Incompressible Viscous Fluids

Print ISBN: 978-3-030-78658-8

Electronic ISBN: 978-3-030-78659-5

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-78659-5_7
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