Symmetry Problems The Navier Stokes Problem
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Symmetry Problems
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Author : Alexander G. Ramm
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Symmetry Problems written by Alexander G. Ramm and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Mathematics categories.
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.
The Navier Stokes Problem
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Author : Alexander G. Ramm
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
The Navier Stokes Problem written by Alexander G. Ramm and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Mathematics categories.
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 (, ) to the NSP exists for all ≥ 0 and (, ) = 0). It is shown that if the initial data 0() ≢ 0, (,) = 0 and the solution to the NSP exists for all ε R+, then 0() := (, 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 21(R3) × C(R+) is proved, 21(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.
Global Special Regular Solutions To The Navier Stokes Equations In Axially Symmetric Domains Under Boundary Slip Conditions
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Author : Wojciech M. Zajączkowski
language : en
Publisher:
Release Date : 2005
Global Special Regular Solutions To The Navier Stokes Equations In Axially Symmetric Domains Under Boundary Slip Conditions written by Wojciech M. Zajączkowski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Boundary value problems categories.
Fundamental Problematic Issues In Turbulence
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Author : Albert Gyr
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Fundamental Problematic Issues In Turbulence written by Albert Gyr and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The Second Monte Verita Colloquium Fundamental Problematic Issues in Turbu lence was held in Monte Verita, Switzerland, on March 23-27, 1998. The main goal of the Colloquium was to bring together in the relaxed atmo sphere of Monte Verita a group of leading scientists (consisting of representatives of different generations) and to discuss informally and free of the influence of funding agencies and/or other "politics" of nonscientific nature the basic issues of turbulence. The intention was to put major emphasis on the exposition of the problematic aspects and discussion(s) - not mere reporting of results, i. e. not hav ing just one more meeting. For this purpose it was originally thought to leave all the afternoons free of formal presentations at all. However, this intention became unrealistic due to a number of reasons, and, in the first place, due to strong pres sure from various parts of the scientific community and non-scientific constraints to broaden the scope and to increase the number of participants as compared to the First Colloquium held in 1991. This resulted in a considerable reduction of time for discussions. Nevertheless, the remaining time for discussions was much larger than usually allocated at scientific conferences. On the scientific side the main idea was to bring together scientists work ing in turbulence from different fields, such as mathematics, physics, engineering and others. In this respect the Colloquium was definitely very successful and re sulted in a number of interesting interactions and contacts.
Analysis Of Weakly Compressible Turbulence Using Symmetry Methods And Direct Numerical Simulation
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Author : Raphael Gotthard Harald Arlitt
language : en
Publisher: Cuvillier Verlag
Release Date : 2005
Analysis Of Weakly Compressible Turbulence Using Symmetry Methods And Direct Numerical Simulation written by Raphael Gotthard Harald Arlitt and has been published by Cuvillier Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Inverse Obstacle Scattering With Non Over Determined Scattering Data
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Author : Alexander G. Ramm
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Inverse Obstacle Scattering With Non Over Determined Scattering Data written by Alexander G. Ramm and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Mathematics categories.
The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering (;;), where (;;) is the scattering amplitude, ; 2 is the direction of the scattered, incident wave, respectively, 2 is the unit sphere in the R3 and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensionality one understands the minimal number of variables of a function describing the data or an object. In an inverse obstacle scattering problem this number is 2, and an example of non-over-determined data is () := (;0;0). By sub-index 0 a fixed value of a variable is denoted. It is proved in this book that the data (), known for all in an open subset of 2, determines uniquely the surface and the boundary condition on . This condition can be the Dirichlet, or the Neumann, or the impedance type. The above uniqueness theorem is of principal importance because the non-over-determined data are the minimal data determining uniquely the unknown . There were no such results in the literature, therefore the need for this book arose. This book contains a self-contained proof of the existence and uniqueness of the scattering solution for rough surfaces.
Lecture Notes On Regularity Theory For The Navier Stokes Equations
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Author : Gregory Seregin
language : en
Publisher: World Scientific
Release Date : 2014-09-16
Lecture Notes On Regularity Theory For The Navier Stokes Equations written by Gregory Seregin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-16 with Mathematics categories.
The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations.The global unique solvability (well-posedness) of initial boundary value problems for the Navier-Stokes equations is in fact one of the seven Millennium problems stated by the Clay Mathematical Institute in 2000. It has not been solved yet. However, a deep connection between regularity and well-posedness is known and can be used to attack the above challenging problem. This type of approach is not very well presented in the modern books on the mathematical theory of the Navier-Stokes equations. Together with introduction chapters, the lecture notes will be a self-contained account on the topic from the very basic stuff to the state-of-art in the field.
Computational Structural Mechanics Fluid Dynamics
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Author : A.K. Noor
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Computational Structural Mechanics Fluid Dynamics written by A.K. Noor 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 Technology & Engineering categories.
Computational structural mechanics (CSM) and computational fluid dynamics (CFD) have emerged in the last two decades as new disciplines combining structural mechanics and fluid dynamics with approximation theory, numerical analysis and computer science. Their use has transformed much of theoretical mechanics and abstract science into practical and essential tools for a multitude of technological developments which affect many facets of our life. This collection of over 40 papers provides an authoritative documentation of major advances in both CSM and CFD, helping to identify future directions of development in these rapidly changing fields. Key areas covered are fluid structure interaction and aeroelasticity, CFD technology and reacting flows, micromechanics, stability and eigenproblems, probabilistic methods and chaotic dynamics, perturbation and spectral methods, element technology (finite volume, finite elements and boundary elements), adaptive methods, parallel processing machines and applications, and visualization, mesh generation and artificial intelligence interfaces.
Mathematics Unlimited 2001 And Beyond
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Author : Björn Engquist
language : en
Publisher: Springer
Release Date : 2017-04-05
Mathematics Unlimited 2001 And Beyond written by Björn Engquist and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-05 with Mathematics categories.
This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.