The Steady Navier Stokes System

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The Steady Navier Stokes System

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Author : Mikhail Korobkov
language : en
Publisher: Springer Nature
Release Date : 2024

The Steady Navier Stokes System written by Mikhail Korobkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Differential equations categories.

Zusammenfassung: This book provides a successful solution to one of the central problems of mathematical fluid mechanics: the Leray's problem on existence of a solution to the boundary value problem for the stationary Navier--Stokes system in bounded domains under sole condition of zero total flux. This marks the culmination of the authors' work over the past few years on this under-explored topic within the study of the Navier--Stokes equations. This book will be the first major work on the Navier--Stokes equations to explore Leray's problem in detail. The results are presented with detailed proofs, as are the history of the problem and the previous approaches to finding a solution to it. In addition, for the reader's convenience and for the self-sufficiency of the text, the foundations of the mathematical theory for incompressible fluid flows described by the steady state Stokes and Navier--Stokes systems are presented. For researchers in this active area, this book will be a valuable resource

Equations Of Motion For Incompressible Viscous Fluids

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Author : Tujin Kim
language : en
Publisher: Springer Nature
Release Date : 2021-09-09

Equations Of Motion For Incompressible Viscous Fluids written by Tujin Kim and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-09 with Mathematics categories.

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.

Theory Of The Navier Stokes Equations

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Author : John Groves Heywood
language : en
Publisher: World Scientific
Release Date : 1998

Theory Of The Navier Stokes Equations written by John Groves Heywood and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

This volume collects the articles presented at the Third International Conference on ?The Navier-Stokes Equations: Theory and Numerical Methods?, held in Oberwolfach, Germany. The articles are important contributions to a wide variety of topics in the Navier-Stokes theory: general boundary conditions, flow exterior to an obstacle, conical boundary points, the controllability of solutions, compressible flow, non-Newtonian flow, magneto-hydrodynamics, thermal convection, the interaction of fluids with elastic solids, the regularity of solutions, and Rothe's method of approximation.

An Introduction To The Mathematical Theory Of The Navier Stokes Equations

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Author : Giovanni P. Galdi
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-07-31

An Introduction To The Mathematical Theory Of The Navier Stokes Equations written by Giovanni P. Galdi 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 1998-07-31 with Science categories.

Undoubtedly, the Navier-Stokes equations are of basic importance within the context of modern theory of partial differential equations. Although the range of their applicability to concrete problems has now been clearly recognised to be limited, as my dear friend and bright colleague K.R. Ra jagopal has showed me by several examples during the past six years, the mathematical questions that remain open are of such a fascinating and challenging nature that analysts and applied mathematicians cannot help being attracted by them and trying to contribute to their resolution. Thus, it is not a coincidence that over the past ten years more than seventy sig nificant research papers have appeared concerning the well-posedness of boundary and initial-boundary value problems. In this monograph I shall perform a systematic and up-to-date investiga tion of the fundamental properties of the Navier-Stokes equations, including existence, uniqueness, and regularity of solutions and, whenever the region of flow is unbounded, of their spatial asymptotic behavior. I shall omit other relevant topics like boundary layer theory, stability, bifurcation, de tailed analysis of the behavior for large times, and free-boundary problems, which are to be considered "advanced" ones. In this sense the present work should be regarded as "introductory" to the matter.

Examination Of The Solutions Of The Navier Stokes Equations For A Class Of Three Dimensional Vortices

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Author : Coleman duP. Donaldson
language : en
Publisher:
Release Date : 1960

Examination Of The Solutions Of The Navier Stokes Equations For A Class Of Three Dimensional Vortices written by Coleman duP. Donaldson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Navier-Stokes equations categories.

Tangential Boundary Stabilization Of Navier Stokes Equations

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Author : Viorel Barbu
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Tangential Boundary Stabilization Of Navier Stokes Equations written by Viorel Barbu 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 2006 with Mathematics categories.

In order to inject dissipation as to force local exponential stabilization of the steady-state solutions, an Optimal Control Problem (OCP) with a quadratic cost functional over an infinite time-horizon is introduced for the linearized N-S equations. As a result, the same Riccati-based, optimal boundary feedback controller which is obtained in the linearized OCP is then selected and implemented also on the full N-S system. For $d=3$, the OCP falls definitely outside the boundaries of established optimal control theory for parabolic systems with boundary controls, in that the combined index of unboundedness--between the unboundedness of the boundary control operator and the unboundedness of the penalization or observation operator--is strictly larger than $\tfrac{3}{2}$, as expressed in terms of fractional powers of the free-dynamics operator. In contrast, established (and rich) optimal control theory [L-T.2] of boundary control parabolic problems and corresponding algebraic Riccati theory requires a combined index of unboundedness strictly less than 1. An additional preliminary serious difficulty to overcome lies at the outset of the program, in establishing that the present highly non-standard OCP--with the aforementioned high level of unboundedness in control and observation operators and subject, moreover, to the additional constraint that the controllers be pointwise tangential--be non-empty; that is, it satisfies the so-called Finite Cost Condition [L-T.2].

Navier Stokes Equations In Planar Domains

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Author : Matania Ben-artzi
language : en
Publisher: World Scientific
Release Date : 2013-03-07

Navier Stokes Equations In Planar Domains written by Matania Ben-artzi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Mathematics categories.

This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as “driven cavity” and “double-driven cavity”.A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a “pure streamfunction” approach. In particular, a complete proof of convergence is given for the full nonlinear problem.This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics./a

On The Existence Of Solutions Of The Steady State Navier Stokes Equations For A Class Of Non Smooth Boundary Data

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Author : James Eugene Edwards
language : en
Publisher:
Release Date : 1963

On The Existence Of Solutions Of The Steady State Navier Stokes Equations For A Class Of Non Smooth Boundary Data written by James Eugene Edwards and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Boundary value problems categories.

Navier Stokes Fourier Equations

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Author : Radyadour Kh. Zeytounian
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-26

Navier Stokes Fourier Equations written by Radyadour Kh. Zeytounian 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 2012-01-26 with Technology & Engineering categories.

This research monograph deals with a modeling theory of the system of Navier-Stokes-Fourier equations for a Newtonian fluid governing a compressible viscous and heat conducting flows. The main objective is threefold. First , to 'deconstruct' this Navier-Stokes-Fourier system in order to unify the puzzle of the various partial simplified approximate models used in Newtonian Classical Fluid Dynamics and this, first facet, have obviously a challenging approach and a very important pedagogic impact on the university education. The second facet of the main objective is to outline a rational consistent asymptotic/mathematical theory of the of fluid flows modeling on the basis of a typical Navier-Stokes-Fourier initial and boundary value problem. The third facet is devoted to an illustration of our rational asymptotic/mathematical modeling theory for various technological and geophysical stiff problems from: aerodynamics, thermal and thermocapillary convections and also meteofluid dynamics.

Exact Solutions To The Navier Stokes Equations With Curl Free Convective Accelerations

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Author : Sheldon Weinbaum
language : en
Publisher:
Release Date : 1966

Exact Solutions To The Navier Stokes Equations With Curl Free Convective Accelerations written by Sheldon Weinbaum and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Fluid mechanics categories.