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Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids Read chapter Read first chapter

2018 | OriginalPaper | Chapter

43. Well-Posedness of the IBVPs for the 1D Viscous Gas Equations

Author : Alexander Zlotnik

Published in: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Publisher: Springer International Publishing

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Abstract

The inhomogeneous initial-boundary value problems (IBVPs) are posed for the Navier-Stokes systems of equations describing the viscous barotropic and heat-conducting gas 1D flow in the Lagrangian mass coordinates. Weak solutions are studied without any restrictions on the magnitude of norms of data. Assumptions on the data are genuinely general, in particular, the initial data are taken from the Lebesgue spaces, the contact problems for different gases are covered, etc. Both the global in time existence of the weak solutions as well as their uniqueness and Lipschitz continuous dependence on data are proved thus ensuring the well-posedness of the IBVPs. The regularity issue is studied as well.

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previous chapter Well-Posedness and Asymptotic Behavior for Compressible Flows in One Dimension
next chapter Waves in Compressible Fluids: Viscous Shock, Rarefaction, and Contact Waves
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Metadata
Title
Well-Posedness of the IBVPs for the 1D Viscous Gas Equations
Author
Alexander Zlotnik
Copyright Year
2018
Book
Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Print ISBN: 978-3-319-13343-0

Electronic ISBN: 978-3-319-13344-7

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-13344-7_33

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