An Introduction To Navier Stokes Equation And Oceanography
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An Introduction To Navier Stokes Equation And Oceanography
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Author : Luc Tartar
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-25
An Introduction To Navier Stokes Equation And Oceanography written by Luc Tartar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-25 with Mathematics categories.
This text corresponds to a graduate mathematics course taught at Carnegie Mellon University in the spring of 1999. Included are comments added to the lecture notes, a bibliography containing 23 items, and brief biographical information for all scientists mentioned in the text, thus showing that the creation of scientific knowledge is an international enterprise.
An Introduction To Sobolev Spaces And Interpolation Spaces
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Author : Luc Tartar
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-26
An Introduction To Sobolev Spaces And Interpolation Spaces written by Luc Tartar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-26 with Mathematics categories.
After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.
Navier Stokes Equations
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Author : Grzegorz Łukaszewicz
language : en
Publisher: Springer
Release Date : 2018-04-22
Navier Stokes Equations written by Grzegorz Łukaszewicz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-22 with Mathematics categories.
This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from advanced undergraduate students to engineers and professional 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.
Introduction To Mathematical Fluid Dynamics
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Author : Richard E. Meyer
language : en
Publisher: Courier Corporation
Release Date : 2012-03-09
Introduction To Mathematical Fluid Dynamics written by Richard E. Meyer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-09 with Science categories.
Excellent coverage of kinematics, momentum principle, Newtonian fluid, rotating fluids, compressibility, and more. Geared toward advanced undergraduate and graduate students of mathematics and science; prerequisites include calculus and vector analysis. 1971 edition.
Physical Oceanography
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Author : Reza Malek-Madani
language : en
Publisher:
Release Date : 2024-10-14
Physical Oceanography written by Reza Malek-Madani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-14 with Mathematics categories.
Accessible to advanced undergraduate students, this text demonstrates how to use the basic tenets of multivariate calculus to derive the governing equations of fluid dynamics in a rotating frame. It also explains how to use linear algebra and PDEs to solve basic initial-boundary value problems that have become the hallmark of physical oceanograp
Mathematical Tools For The Study Of The Incompressible Navier Stokes Equations Andrelated Models
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Author : Franck Boyer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-06
Mathematical Tools For The Study Of The Incompressible Navier Stokes Equations Andrelated Models written by Franck Boyer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-06 with Mathematics categories.
The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject. .
Regularity Theory For Generalized Navier Stokes Equations
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Author : Cholmin Sin
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-17
Regularity Theory For Generalized Navier Stokes Equations written by Cholmin Sin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-17 with Mathematics categories.
This book delves into the recent findings and research methods in the existence and regularity theory for Non-Newtonian Fluids with Variable Power-Law. The aim of this book is not only to introduce recent results and research methods in the existence and regularity theory, such as higher integrability, higher differentiability, and Holder continuity for flows of non-Newtonian fluids with variable power-laws, but also to summarize much of the existing literature concerning these topics. While this book mainly focuses on steady-state flows of non-Newtonian fluids, the methods and ideas presented in this book can be applied to unsteady flows (as discussed in Chapter 7) and other related problems such as complex non-Newtonian fluids, plasticity, elasticity, p(x)-Laplacian type systems, and so on. The book is intended for researchers and graduate students in the field of mathematical fluid mechanics and partial differential equations with variable exponents. It is expected to contribute to the advancement of mathematics and its applications.
Navier Stokes Equations
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Author : Roger Temam
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-04-10
Navier Stokes Equations written by Roger Temam and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-10 with Mathematics categories.
Originally published in 1977, the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the theoretical side, results related to the existence, the uniqueness, and, in some cases, the regularity of solutions are presented. On the numerical side, various approaches to the approximation of Navier-Stokes problems by discretization are considered, such as the finite dereference method, the finite element method, and the fractional steps method. The problems of stability and convergence for numerical methods are treated as completely as possible. The new material in the present book (as compared to the preceding 1984 edition) is an appendix reproducing a survey article written in 1998. This appendix touches upon a few aspects not addressed in the earlier editions, in particular a short derivation of the Navier-Stokes equations from the basic conservation principles in continuum mechanics, further historical perspectives, and indications on new developments in the area. The appendix also surveys some aspects of the related Euler equations and the compressible Navier-Stokes equations. The book is written in the style of a textbook and the author has attempted to make the treatment self-contained. It can be used as a textbook or a reference book for researchers. Prerequisites for reading the book include some familiarity with the Navier-Stokes equations and some knowledge of functional analysis and Sololev spaces.
Linear And Nonlinear Functional Analysis With Applications
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Author : Philippe G. Ciarlet
language : en
Publisher: SIAM
Release Date : 2013-10-10
Linear And Nonlinear Functional Analysis With Applications written by Philippe G. Ciarlet and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-10 with Mathematics categories.
This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.
Introductory Dynamical Oceanography
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Author : Stephen Pond
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Introductory Dynamical Oceanography written by Stephen Pond and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
'Introductory Dynamical Oceanography' 2nd ed provides an introduction to Dynamical Physical Oceanography at a level suitable for senior year undergraduate students in the sciences and for graduate students entering oceanography. It aims to present the basic objectives, procedures and successes and to state some of the present limitations of dynamical oceanography and its relations to descriptive physical oceanography. The first edition has been thoroughly revised and updated and the new work includes reference to the Practical Salinity Scale 1978, the International Equation of State 1980 and the beta-spiral technique for calculating absolute currents from the density distribution. In addition the description of mixed-layer models has been updated and the chapters on Waves and on Tides have been substantially revised and enlarged, with emphasis on internal waves in the Waves chapter. While the text is self-contained readers are recommended to acquaint themselves with the general aspects of descriptive (synoptic) oceanography in order to be aware of the character of the ocean which the dynamical oceanographer is attempting to explain by referring to Pickard and Emery's 'Descriptive Physical Oceanography' 4th edition.