Overview
- Presents a variety of boundary conditions for fluids while taking into special account the properties of boundaries of vector fields on domains
- Highlights how fluid equations at the cutting edge of research were developed and how certain boundary conditions apply to various real-world problems
- Adopts a self-contained approach that covers introductory topics as well as more advanced material, such as friction conditions and a thorough outline of the Navier-Stokes equations
Part of the book series: Advances in Mathematical Fluid Mechanics (AMFM)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
- Fluid mechanics friction boundary
- Steady Boussinesq system
- Heat-conducting fluids
- Mixed boundary conditions
- Variational inequality fluid mechanics
- Stress boundary conditions
- Pressure boundary conditions
- Vorticity boundary conditions
- Tresca slip boundary conditions
- Leak boundary conditions
- Navier-Stokes equations
- Navier-Stokes non-steady
- Navier-Stokes steady
- Lebesgue space fluid mechanics
- Sobolev space fluid mechanics
- Banach space fluid mechanics
About this book
This monograph explores the motion of incompressible fluids by presenting and incorporating various boundary conditions possible for real phenomena. The authors’ approach carefully walks readers through the development of fluid equations at the cutting edge of research, and the applications of a variety of boundary conditions to real-world problems. Special attention is paid to the equivalence between partial differential equations with a mixture of various boundary conditions and their corresponding variational problems, especially variational inequalities with one unknown. A self-contained approach is maintained throughout by first covering introductory topics, and then moving on to mixtures of boundary conditions, a thorough outline of the Navier-Stokes equations, an analysis of both the steady and non-steady Boussinesq system, and more. Equations of Motion for Incompressible Viscous Fluids is ideal for postgraduate students and researchers in the fields of fluid equations, numerical analysis, and mathematical modelling.
Authors and Affiliations
Bibliographic Information
Book Title: Equations of Motion for Incompressible Viscous Fluids
Book Subtitle: With Mixed Boundary Conditions
Authors: Tujin Kim, Daomin Cao
Series Title: Advances in Mathematical Fluid Mechanics
DOI: https://doi.org/10.1007/978-3-030-78659-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-78658-8Published: 10 September 2021
Softcover ISBN: 978-3-030-78661-8Published: 10 September 2022
eBook ISBN: 978-3-030-78659-5Published: 09 September 2021
Series ISSN: 2297-0320
Series E-ISSN: 2297-0339
Edition Number: 1
Number of Pages: XIII, 364
Number of Illustrations: 1 b/w illustrations
Topics: Analysis, Optimization, Functional Analysis