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2018 | OriginalPaper | Chapter

45. Existence of Stationary Weak Solutions for Isentropic and Isothermal Compressible Flows

Authors : Song Jiang, Chunhui Zhou

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

Publisher: Springer International Publishing

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Abstract

The aim of this chapter is to study the existence of weak solutions to the multidimensional steady isentropic and isothermal compressible Navier-Stokes equations with large external forces. In the past decades, significant progress has been made on the existence of large weak solutions. In this chapter, a brief review of recent existence results on the existence of (renormalized) stationary weak solutions with large external forces will be presented. Different boundary value problems, such as the spatially periodic, slip and Dirichlet boundary value problems, will be investigated, and some related topics such as nonuniqueness, regularity, etc., will also be discussed. The ideas and developed techniques used in analysis will be presented and analyzed, and some open problems will be addressed.

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Title: Existence of Stationary Weak Solutions for Isentropic and Isothermal Compressible Flows
Authors: Song Jiang
Chunhui Zhou
Publisher: Springer International Publishing
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_63

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