Recent developments in the Navier-Stokes problem, Lemarie-Rieusset, Pierre
Автор: Khots Boris Название: Observability and Mathematics: Fluid Mechanics, Solutions of Navier-Stokes Equations, and Modeling ISBN: 103200813X ISBN-13(EAN): 9781032008134 Издательство: Taylor&Francis Рейтинг: Цена: 112290.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The author approaches an old classic problem - the existence of solutions of Navier-Stokes eqs. The main objective is to model and derive of equation of continuity, Euler equation of fluid motion, energy flux equation, Navier-Stokes eqs from the observer point of view and solve classic problem for this interpretation of fluid motion laws.
Автор: Lemarie-rieusset, Pierre Gilles Название: Navier-stokes problem in the 21st century ISBN: 0367658577 ISBN-13(EAN): 9780367658571 Издательство: Taylor&Francis Рейтинг: Цена: 40820.00 T Наличие на складе: Нет в наличии. Описание: This book focuses on incompressible deterministic Navier-Stokes equations in the case of a fluid filling the whole space. It explores the meaning of the equations, open problems, and recent progress. It includes classical results on local existence and studies criterion for regularity or uniqueness of solutions. The book also incorporates histor
Автор: Lemarie-Rieusset, Pierre Gilles Название: The Navier-Stokes Problem in the 21st Century ISBN: 0367487268 ISBN-13(EAN): 9780367487263 Издательство: Taylor&Francis Рейтинг: Цена: 112290.00 T Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Ramm Alexander G. Название: Symmetry Problems. the Navier-Stokes Problem. ISBN: 1681735059 ISBN-13(EAN): 9781681735054 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 41580.00 T Наличие на складе: Невозможна поставка. Описание: This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of ""invisible obstacles."" In Chapter 5, it provides a solution to the Navier‒Stokes problem in ℝ³. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier‒Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies.
Автор: Ramm Alexander G. Название: Symmetry Problems. the Navier-Stokes Problem. ISBN: 1681735075 ISBN-13(EAN): 9781681735078 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 61910.00 T Наличие на складе: Невозможна поставка. Описание: This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of ""invisible obstacles."" In Chapter 5, it provides a solution to the Navier‒Stokes problem in ℝ³. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier‒Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies.
Автор: Joanna Renc?awowicz; Wojciech M. Zaj?czkowski Название: The Large Flux Problem to the Navier-Stokes Equations ISBN: 3030323293 ISBN-13(EAN): 9783030323295 Издательство: Springer Рейтинг: Цена: 65210.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This monograph considers the motion of incompressible fluids described by the Navier-Stokes equations with large inflow and outflow, and proves the existence of global regular solutions without any restrictions on the magnitude of the initial velocity, the external force, or the flux. To accomplish this, some assumptions are necessary: The flux is close to homogeneous, and the initial velocity and the external force do not change too much along the axis of the cylinder. This is achieved by utilizing a sophisticated method of deriving energy type estimates for weak solutions and global estimates for regular solutions—an approach that is wholly unique within the existing literature on the Navier-Stokes equations. To demonstrate these results, three main steps are followed: first, the existence of weak solutions is shown; next, the conditions guaranteeing the regularity of weak solutions are presented; and, lastly, global regular solutions are proven. This volume is ideal for mathematicians whose work involves the Navier-Stokes equations, and, more broadly, researchers studying fluid mechanics.
Автор: Ramm Alexander G. Название: The Navier-Stokes Problem ISBN: 1636391222 ISBN-13(EAN): 9781636391229 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 37890.00 T Наличие на складе: Поставка под заказ. Описание: The main result of this book is a proof of the contradictory nature of the Navier‒Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on ℝ+ (except for the case when the initial velocity and the exterior force are both equal to zero; in this case, the solution 𝑣(𝑥, 𝑡) to the NSP exists for all 𝑡 ≥ 0 and 𝑣(𝑥, 𝑡) = 0).
It is shown that if the initial data 𝑣0(𝑥) ≢ 0, 𝑓(𝑥,𝑡) = 0 and the solution to the NSP exists for all 𝑡 ϵ ℝ+, then 𝑣0(𝑥) := 𝑣(𝑥, 0) = 0.
This Paradox proves that the NSP is physically incorrect and mathematically unsolvable, in general. Uniqueness of the solution to the NSP in the space 𝑊21(ℝ3) × C(ℝ+) is proved, 𝑊21(ℝ3) is the Sobolev space, ℝ+ = [0, ∞).
Theory of integral equations and inequalities with hyper-singular kernels is developed. The NSP is reduced to an integral inequality with a hyper-singular kernel.
Автор: Ramm Alexander G. Название: The Navier-Stokes Problem ISBN: 1636391249 ISBN-13(EAN): 9781636391243 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 59130.00 T Наличие на складе: Поставка под заказ. Описание:
The main result of this book is a proof of the contradictory nature of the Navier‒Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on ℝ+ (except for the case when the initial velocity and the exterior force are both equal to zero; in this case, the solution 𝑣(𝑥, 𝑡) to the NSP exists for all 𝑡 ≥ 0 and 𝑣(𝑥, 𝑡) = 0).
It is shown that if the initial data 𝑣0(𝑥) ≢ 0, 𝑓(𝑥,𝑡) = 0 and the solution to the NSP exists for all 𝑡 ϵ ℝ+, then 𝑣0(𝑥) := 𝑣(𝑥, 0) = 0.
This Paradox proves that the NSP is physically incorrect and mathematically unsolvable, in general. Uniqueness of the solution to the NSP in the space 𝑊21(ℝ3) × C(ℝ+) is proved, 𝑊21(ℝ3) is the Sobolev space, ℝ+ = [0, ∞).
Theory of integral equations and inequalities with hyper-singular kernels is developed. The NSP is reduced to an integral inequality with a hyper-singular kernel.
Автор: Robinson Название: Recent Progress in the Theory of the Euler and Navier–Stokes Equations ISBN: 1107554977 ISBN-13(EAN): 9781107554979 Издательство: Cambridge Academ Рейтинг: Цена: 61240.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This survey volume provides an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. It serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.
Автор: Hermann Sohr Название: The Navier-Stokes Equations ISBN: 3034805500 ISBN-13(EAN): 9783034805506 Издательство: Springer Рейтинг: Цена: 121110.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book develops an elementary and self-contained approach to the mathematical theory of a viscous, incompressible fluid in a domain of the Euclidean space, described by the equations of Navier-Stokes.
Автор: Lemarie-Rieusset Название: Navier-Stokes Prob In 21St Century ISBN: 1466566213 ISBN-13(EAN): 9781466566217 Издательство: Taylor&Francis Рейтинг: Цена: 96970.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Up-to-Date Coverage of the Navier-Stokes Equation from an Expert in Harmonic Analysis
The complete resolution of the Navier-Stokes equation--one of the Clay Millennium Prize Problems--remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier-Stokes Problem in the 21st Century provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics.
The book focuses on incompressible deterministic Navier-Stokes equations in the case of a fluid filling the whole space. It explores the meaning of the equations, open problems, and recent progress. It includes classical results on local existence and studies criterion for regularity or uniqueness of solutions. The book also incorporates historical references to the (pre)history of the equations as well as recent references that highlight active mathematical research in the field.
Автор: Jacob Bedrossian, Vlad Vicol Название: The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations: An Introduction ISBN: 1470471787 ISBN-13(EAN): 9781470471781 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 71060.00 T Наличие на складе: Поставка под заказ. Описание: The aim of this book is to provide beginning graduate students who completed the first two semesters of graduate-level analysis and PDE courses with a first exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces.Chapters 1 and 2 cover the fundamentals of the Euler theory: derivation, Eulerian and Lagrangian perspectives, vorticity, special solutions, existence theory for smooth solutions, and blowup criteria. Chapters 3, 4, and 5 cover the fundamentals of the Navier-Stokes theory: derivation, special solutions, existence theory for strong solutions, Leray theory of weak solutions, weak-strong uniqueness, existence theory of mild solutions, and Prodi-Serrin regularity criteria. Chapter 6 provides a short guide to the must-read topics, including active research directions, for an advanced graduate student working in incompressible fluids. It may be used as a roadmap for a topics course in a subsequent semester. The appendix recalls basic results from real, harmonic, and functional analysis. Each chapter concludes with exercises, making the text suitable for a one-semester graduate course.Prerequisites to this book are the first two semesters of graduate-level analysis and PDE courses.
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