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Analysis of the Navier-Stokes Problem de Alexander G. Ramm

Analysis of the Navier-Stokes Problem: Synthesis Lectures on Mathematics & Statistics

Autor Alexander G. Ramm
en Limba Engleză Hardback – 25 iun 2023
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.
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Specificații

ISBN-13: 9783031307225
ISBN-10: 3031307224
Pagini: 104
Ilustrații: XVI, 87 p. 1 illus.
Dimensiuni: 173 x 246 x 12 mm
Greutate: 0.31 kg
Ediția:Second Edition 2023
Editura: Springer
Colecția Synthesis Lectures on Mathematics & Statistics
Seria Synthesis Lectures on Mathematics & Statistics

Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică

Alexander G. Ramm, Ph.D., was born in Russia, immigrated to the U.S. in 1979, and is a U.S. citizen. He is Professor of Mathematics with broad interests in analysis, scattering theory, inverse problems, theoretical physics, engineering, signal estimation, tomography, theoretical numerical analysis, and applied mathematics. He is an author of 690 research papers, 16 monographs, and an editor of 3 books. He has lectured in many universities throughout the world, presented approximately 150 invited and plenary talks at various conferences, and has supervised 11 Ph.D. students. He was Fulbright Research Professor in Israel and in Ukraine, distinguished visiting professor in Mexico and Egypt, Mercator professor, invited plenary speaker at the 7th PACOM, won the Khwarizmi international award, and received other honors. Recently he solved inverse scattering problems with non-over-determined data and the many-body wave-scattering problem when the scatterers are small particles of an arbitraryshape; Dr. Ramm used this theory to give a recipe for creating materials with a desired refraction coefficient, gave a solution to the refined Pompeiu problem and proved the refined Schiffers conjecture.

Textul de pe ultima copertă

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.