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Analysis of the Navier-Stokes Problem [electronic resource] : Solution of a Millennium Problem / by Alexander G. Ramm.

By: Ramm, Alexander G [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Synthesis Lectures on Mathematics & Statistics: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2023Edition: 2nd ed. 2023.Description: XVI, 87 p. 1 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783031307232.Subject(s): Mathematics | Mathematical logic | Mathematics -- Data processing | Mathematics | Mathematical Logic and Foundations | Computational Mathematics and Numerical Analysis | Applications of MathematicsAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 510 Online resources: Click here to access online
Contents:
Introduction -- Brief History of the Navier-Stokes Problem -- Statement of the Navier-Stokes Problem -- Theory of Some Hyper-Singular Integral Equations -- A Priori Estimates of the Solution to the NSP -- Uniqueness of the Solution to the NSP -- The Paradox and its Consequences -- Logical Analysis of Our Proof.
In: Springer Nature eBookSummary: This book revises and expands upon the prior edition, The Navier-Stokes Problem. The focus of this book is to provide a mathematical analysis of the Navier-Stokes Problem (NSP) in R^3 without boundaries. Before delving into analysis, the author begins by explaining the background and history of the Navier-Stokes Problem. This edition includes new analysis and an a priori estimate of the solution. The estimate proves the contradictory nature of the Navier-Stokes Problem. The author reaches the conclusion that the solution to the NSP with smooth and rapidly decaying data cannot exist for all positive times. By proving the NSP paradox, this book provides a solution to the millennium problem concerning the Navier-Stokes Equations and shows that they are physically and mathematically contradictive. In addition, this book: Explains the background and history of the Navier-Stokes Problem Provides mathematical analysis of the Navier-Stokes Problem in R3 without boundaries Proves that the Navier-Stokes equations are physically and mathematically contradictive About the Author: Alexander G. Ramm, Ph.D., is a Professor Emeritus of Mathematics at Kansas State University. He is the author of approximately 715 research papers, 20 research monographs, and an editor of three books. Dr. Ramm won the Khwarizmi international award in 2004. His research interests include analysis, scattering theory, inverse problems, theoretical physics, engineering, signal estimation, tomography, theoretical numerical analysis, and applied mathematics.
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Introduction -- Brief History of the Navier-Stokes Problem -- Statement of the Navier-Stokes Problem -- Theory of Some Hyper-Singular Integral Equations -- A Priori Estimates of the Solution to the NSP -- Uniqueness of the Solution to the NSP -- The Paradox and its Consequences -- Logical Analysis of Our Proof.

This book revises and expands upon the prior edition, The Navier-Stokes Problem. The focus of this book is to provide a mathematical analysis of the Navier-Stokes Problem (NSP) in R^3 without boundaries. Before delving into analysis, the author begins by explaining the background and history of the Navier-Stokes Problem. This edition includes new analysis and an a priori estimate of the solution. The estimate proves the contradictory nature of the Navier-Stokes Problem. The author reaches the conclusion that the solution to the NSP with smooth and rapidly decaying data cannot exist for all positive times. By proving the NSP paradox, this book provides a solution to the millennium problem concerning the Navier-Stokes Equations and shows that they are physically and mathematically contradictive. In addition, this book: Explains the background and history of the Navier-Stokes Problem Provides mathematical analysis of the Navier-Stokes Problem in R3 without boundaries Proves that the Navier-Stokes equations are physically and mathematically contradictive About the Author: Alexander G. Ramm, Ph.D., is a Professor Emeritus of Mathematics at Kansas State University. He is the author of approximately 715 research papers, 20 research monographs, and an editor of three books. Dr. Ramm won the Khwarizmi international award in 2004. His research interests include analysis, scattering theory, inverse problems, theoretical physics, engineering, signal estimation, tomography, theoretical numerical analysis, and applied mathematics.

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