The Navier-Stokes Problem, Ramm Alexander G.

Автор: Ramm Alexander G.
Название: The Navier-Stokes Problem
ISBN: 1636391249 ISBN-13(EAN): 9781636391243
Издательство: Mare Nostrum (Eurospan)
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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: Symmetry Problems. the Navier-Stokes Problem.
ISBN: 1681735059 ISBN-13(EAN): 9781681735054
Издательство: Mare Nostrum (Eurospan)
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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)
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Цена: 61910.00 T
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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
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Цена: 65210.00 T
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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: Ben Artzi Matania
Название: Navier-Stokes Equations in Planar Domains
ISBN: 1848162758 ISBN-13(EAN): 9781848162754
Издательство: World Scientific Publishing
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Описание: Deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. This book describes various 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`.

Автор: Robinson
Название: The Three-Dimensional Navier–Stokes Equations
ISBN: 1107019664 ISBN-13(EAN): 9781107019669
Издательство: Cambridge Academ
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Описание: A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier-Stokes equations, offering a self-contained treatment of many of the major results. Numerous exercises are provided, each with full solutions, making the book an ideal text for a graduate course of one or two semesters.

Автор: L. Stupelis
Название: Navier-Stokes Equations in Irregular Domains
ISBN: 0792335090 ISBN-13(EAN): 9780792335092
Издательство: Springer
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Цена: 139310.00 T
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Описание: The analytical basis of Navier-Stokes Equations in Irregular Domains is formed by coercive estimates, which enable proofs to be given of the solvability of the boundary value problems for Stokes and Navier-Stokes equations in weighted Sobolev and Holder spaces, and the investigation of the smoothness of their solutions.

Автор: Giovanni Galdi
Название: An Introduction to the Mathematical Theory of the Navier-Stokes Equations
ISBN: 1493950177 ISBN-13(EAN): 9781493950171
Издательство: Springer
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Описание: The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations. This book is the new edition of the original two volume book, under the same title, published in 1994.

Автор: Stenger Frank, Tucker Don, Baumann Gerd
Название: Navier-Stokes Equations on R3 Ч [0, T]
ISBN: 3319801627 ISBN-13(EAN): 9783319801629
Издательство: Springer
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Цена: 93160.00 T
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Описание: Preface.- Introduction, PDE, and IE Formulations.- Spaces of Analytic Functions.- Spaces of Solution of the N-S Equations.- Proof of Convergence of Iteration 1.6.3.- Numerical Methods for Solving N-S Equations.- Sinc Convolution Examples.- Implementation Notes.- Result Notes.

Автор: Viorel Barbu
Название: Stabilization of Navier–Stokes Flows
ISBN: 1447126106 ISBN-13(EAN): 9781447126102
Издательство: Springer
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Цена: 104480.00 T
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Описание: Stabilization of Navier-Stokes Flows presents recent notable progress in the mathematical theory of stabilization of Newtonian fluid flows.

Автор: Ad?lia Sequeira
Название: Navier—Stokes Equations and Related Nonlinear Problems
ISBN: 0306451182 ISBN-13(EAN): 9780306451188
Издательство: Springer
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Цена: 148020.00 T
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Описание: This volume contains the Proceedings of the Third International Conference on Navier-Stokes Equations and Related Nonlinear Problems. In addition to the editor, the organizers were Carlos Albuquerque (FC, University of Lisbon), Casimiro Silva (University of Madeira) and Juha Videman (1ST, Technical University of Lisbon).

Автор: Hermann Sohr
Название: The Navier-Stokes Equations
ISBN: 3034805500 ISBN-13(EAN): 9783034805506
Издательство: Springer
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Цена: 121110.00 T
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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.