Cargando…

Navier-Stokes equations: an introduction with applications

This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowled...

Descripción completa

Detalles Bibliográficos
Autores principales: Łukaszewicz, Grzegorz, Kalita, Piotr
Lenguaje:eng
Publicado: Springer 2016
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-27760-8
http://cds.cern.ch/record/2151737
_version_ 1780950496123551744
author Łukaszewicz, Grzegorz
Kalita, Piotr
author_facet Łukaszewicz, Grzegorz
Kalita, Piotr
author_sort Łukaszewicz, Grzegorz
collection CERN
description This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier–Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.
id cern-2151737
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2016
publisher Springer
record_format invenio
spelling cern-21517372021-04-21T19:42:29Zdoi:10.1007/978-3-319-27760-8http://cds.cern.ch/record/2151737engŁukaszewicz, GrzegorzKalita, PiotrNavier-Stokes equations: an introduction with applicationsMathematical Physics and MathematicsThis volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier–Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.Springeroai:cds.cern.ch:21517372016
spellingShingle Mathematical Physics and Mathematics
Łukaszewicz, Grzegorz
Kalita, Piotr
Navier-Stokes equations: an introduction with applications
title Navier-Stokes equations: an introduction with applications
title_full Navier-Stokes equations: an introduction with applications
title_fullStr Navier-Stokes equations: an introduction with applications
title_full_unstemmed Navier-Stokes equations: an introduction with applications
title_short Navier-Stokes equations: an introduction with applications
title_sort navier-stokes equations: an introduction with applications
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-27760-8
http://cds.cern.ch/record/2151737
work_keys_str_mv AT łukaszewiczgrzegorz navierstokesequationsanintroductionwithapplications
AT kalitapiotr navierstokesequationsanintroductionwithapplications