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Author : Edriss S. Titi
Publisher :
ISBN 13 :
Total Pages : 72 pages
Book Rating : 4.E/5 ( download)
Download or read book On Approximate Inertial Manifolds to the 2-d Navier-Stokes Equations written by Edriss S. Titi and published by . This book was released on 1988 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Boling Guo
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110549654
Total Pages : 438 pages
Book Rating : 4.1/5 (15 download)
Download or read book Attractors and Inertial Manifolds written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-07-09 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. Contents Attractor and its dimension estimation Inertial manifold The approximate inertial manifold
Author : Zhoude Shao
Publisher :
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.:/5 (319 download)
Download or read book Inertial Manifolds for Partly Dissipative Reaction Diffusion Systems in Higher Space Dimensions written by Zhoude Shao and published by . This book was released on 1994 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Grzegorz Łukaszewicz
Publisher : Springer
ISBN 13 : 331927760X
Total Pages : 395 pages
Book Rating : 4.3/5 (192 download)
Download or read book Navier–Stokes Equations written by Grzegorz Łukaszewicz and published by Springer. This book was released on 2016-04-12 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Roger Temam
Publisher : SIAM
ISBN 13 : 9781611970050
Total Pages : 155 pages
Book Rating : 4.9/5 (7 download)
Download or read book Navier-Stokes Equations and Nonlinear Functional Analysis written by Roger Temam and published by SIAM. This book was released on 1995-01-01 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition, like the first, attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations in the following areas: existence, uniqueness, and regularity of solutions in space dimensions two and three; large time behavior of solutions and attractors; and numerical analysis of the Navier-Stokes equations. Since publication of the first edition of these lectures in 1983, there has been extensive research in the area of inertial manifolds for Navier-Stokes equations. These developments are addressed in a new section devoted entirely to inertial manifolds. Inertial manifolds were first introduced under this name in 1985 and, since then, have been systematically studied for partial differential equations of the Navier-Stokes type. Inertial manifolds are a global version of central manifolds. When they exist they encompass the complete dynamics of a system, reducing the dynamics of an infinite system to that of a smooth, finite-dimensional one called the inertial system. Although the theory of inertial manifolds for Navier-Stokes equations is not complete at this time, there is already a very interesting and significant set of results which deserves to be known, in the hope that it will stimulate further research in this area. These results are reported in this edition.
Author : C. Foias
Publisher : Cambridge University Press
ISBN 13 : 1139428993
Total Pages : 363 pages
Book Rating : 4.1/5 (394 download)
Download or read book Navier-Stokes Equations and Turbulence written by C. Foias and published by Cambridge University Press. This book was released on 2001-08-27 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience.
Author : Katie Coughlin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821895177
Total Pages : 144 pages
Book Rating : 4.8/5 (951 download)
Download or read book Semi-analytic Methods for the Navier-Stokes Equations written by Katie Coughlin and published by American Mathematical Soc.. This book was released on 1999-04-18 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures collected for this volume were given during a workshop entitled, ``Semi-analytic Methods for the Navier Stokes Equations'' held at the CRM in Montreal. The title reflects the current reality in fluid dynamics: Navier-Stokes equations (NSE) describe the behavior of fluid in a wide range of physical situations, the solutions of these equations are sufficiently complicated, so that another level of analysis is clearly needed. The fundamental problem is not just to solve the NSE, but also to understand what the solutions mean. One of the goals of the workshop was to bring together people who, while working in different fields, share a common perspective on the nature of the problem to be solved. The lectures present a diverse set of techniques for modelling, computing, and understanding phenomena such as instabilities, turbulence and spatiotemporal chaos in fluids.
Author : K.D. Elworthy
Publisher : Routledge
ISBN 13 : 1351455206
Total Pages : 1000 pages
Book Rating : 4.3/5 (514 download)
Download or read book Differential Equations written by K.D. Elworthy and published by Routledge. This book was released on 2017-11-22 with total page 1000 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents recent developments in the areas of differential equations, dynamical systems, and control of finke and infinite dimensional systems. Focuses on current trends in differential equations and dynamical system research-from Darameterdependence of solutions to robui control laws for inflnite dimensional systems.
Author : James C. Robinson
Publisher : Cambridge University Press
ISBN 13 : 9780521632041
Total Pages : 488 pages
Book Rating : 4.6/5 (32 download)
Download or read book Infinite-Dimensional Dynamical Systems written by James C. Robinson and published by Cambridge University Press. This book was released on 2001-04-23 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.
Author : Thierry Dubois
Publisher : Cambridge University Press
ISBN 13 : 9780521621656
Total Pages : 314 pages
Book Rating : 4.6/5 (216 download)
Download or read book Dynamic Multilevel Methods and the Numerical Simulation of Turbulence written by Thierry Dubois and published by Cambridge University Press. This book was released on 1999-01-13 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the implementation of multilevel methods in a dynamical context, with application to the numerical simulation of turbulent flows. The general ideas for the algorithms presented stem from dynamical systems theory and are based on the decomposition of the unknown function into two or more arrays corresponding to different scales in the Fourier space. This timely monograph should appeal to graduate students and researchers alike, providing a background for applied mathematicians as well as engineers.
Author : David N Cheban
Publisher : World Scientific
ISBN 13 : 9814481866
Total Pages : 524 pages
Book Rating : 4.8/5 (144 download)
Download or read book Global Attractors Of Nonautonomous Dissipative Dynamical Systems written by David N Cheban and published by World Scientific. This book was released on 2004-11-29 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor. From an in-depth introduction to the different types of dissipativity and attraction, the book takes a comprehensive look at the connections between them, and critically discusses applications of general results to different classes of differential equations. Intended for experts in qualitative theory of differential equations, dynamical systems and their applications, this accessible book can also serve as an important resource for senior students and lecturers.
Author : S. Friedlander
Publisher : Gulf Professional Publishing
ISBN 13 : 008053354X
Total Pages : 627 pages
Book Rating : 4.0/5 (85 download)
Download or read book Handbook of Mathematical Fluid Dynamics written by S. Friedlander and published by Gulf Professional Publishing. This book was released on 2003-03-27 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.
Author :
Publisher :
ISBN 13 :
Total Pages : 568 pages
Book Rating : 4.:/5 (3 download)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mickaël D. Chekroun
Publisher : Springer
ISBN 13 : 331912496X
Total Pages : 136 pages
Book Rating : 4.3/5 (191 download)
Download or read book Approximation of Stochastic Invariant Manifolds written by Mickaël D. Chekroun and published by Springer. This book was released on 2014-12-20 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.
Author : Boling Guo
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110614782
Total Pages : 370 pages
Book Rating : 4.1/5 (16 download)
Download or read book Nonlinear Evolution Equations written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-11-05 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Evolution Equation presents state-of-the-art theories and results on nonlinear evolution equation, showing related mathematical methods and applications. The basic concepts and research methods of infinite dimensional dynamical systems are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and students in applied mathematics and physics.
Author : Jose Manuel Vega
Publisher : Academic Press
ISBN 13 : 0128227664
Total Pages : 322 pages
Book Rating : 4.1/5 (282 download)
Download or read book Higher Order Dynamic Mode Decomposition and Its Applications written by Jose Manuel Vega and published by Academic Press. This book was released on 2020-09-22 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Higher Order Dynamic Mode Decomposition and Its Applications provides detailed background theory, as well as several fully explained applications from a range of industrial contexts to help readers understand and use this innovative algorithm. Data-driven modelling of complex systems is a rapidly evolving field, which has applications in domains including engineering, medical, biological, and physical sciences, where it is providing ground-breaking insights into complex systems that exhibit rich multi-scale phenomena in both time and space. Starting with an introductory summary of established order reduction techniques like POD, DEIM, Koopman, and DMD, this book proceeds to provide a detailed explanation of higher order DMD, and to explain its advantages over other methods. Technical details of how the HODMD can be applied to a range of industrial problems will help the reader decide how to use the method in the most appropriate way, along with example MATLAB codes and advice on how to analyse and present results. - Includes instructions for the implementation of the HODMD, MATLAB codes, and extended discussions of the algorithm - Includes descriptions of other order reduction techniques, and compares their strengths and weaknesses - Provides examples of applications involving complex flow fields, in contexts including aerospace engineering, geophysical flows, and wind turbine design
Author : Hamid Bellout
Publisher : Springer Science & Business Media
ISBN 13 : 3319008919
Total Pages : 583 pages
Book Rating : 4.3/5 (19 download)
Download or read book Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow written by Hamid Bellout and published by Springer Science & Business Media. This book was released on 2013-11-19 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of incompressible multipolar viscous fluids is a non-Newtonian model of fluid flow, which incorporates nonlinear viscosity, as well as higher order velocity gradients, and is based on scientific first principles. The Navier-Stokes model of fluid flow is based on the Stokes hypothesis, which a priori simplifies and restricts the relationship between the stress tensor and the velocity. By relaxing the constraints of the Stokes hypothesis, the mathematical theory of multipolar viscous fluids generalizes the standard Navier-Stokes model. The rigorous theory of multipolar viscous fluids is compatible with all known thermodynamical processes and the principle of material frame indifference; this is in contrast with the formulation of most non-Newtonian fluid flow models which result from ad hoc assumptions about the relation between the stress tensor and the velocity. The higher-order boundary conditions, which must be formulated for multipolar viscous flow problems, are a rigorous consequence of the principle of virtual work; this is in stark contrast to the approach employed by authors who have studied the regularizing effects of adding artificial viscosity, in the form of higher order spatial derivatives, to the Navier-Stokes model. A number of research groups, primarily in the United States, Germany, Eastern Europe, and China, have explored the consequences of multipolar viscous fluid models; these efforts, and those of the authors, which are described in this book, have focused on the solution of problems in the context of specific geometries, on the existence of weak and classical solutions, and on dynamical systems aspects of the theory. This volume will be a valuable resource for mathematicians interested in solutions to systems of nonlinear partial differential equations, as well as to applied mathematicians, fluid dynamicists, and mechanical engineers with an interest in the problems of fluid mechanics.
