Eulerian Spaces
Author: Paul Gartside
Publisher: American Mathematical Society
Published: 2024-01-26
Total Pages: 98
ISBN-13: 1470467844
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Eulerian Spaces
Author: Paul Gartside
Publisher:
Published: 2023
Total Pages: 0
ISBN-13: 9781470477011
DOWNLOAD EBOOK →The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations
Author: Jacob Bedrossian
Publisher: American Mathematical Society
Published: 2022-09-21
Total Pages: 235
ISBN-13: 1470470497
DOWNLOAD EBOOK →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.
Letters of Euler on Different Subjects in Natural Philosophy
Fundamentals of Continuum Mechanics
Author: Stephen Bechtel
Publisher: Academic Press
Published: 2014-12-02
Total Pages: 347
ISBN-13: 0123948347
DOWNLOAD EBOOK →Fundamentals of Continuum Mechanics provides a clear and rigorous presentation of continuum mechanics for engineers, physicists, applied mathematicians, and materials scientists. This book emphasizes the role of thermodynamics in constitutive modeling, with detailed application to nonlinear elastic solids, viscous fluids, and modern smart materials. While emphasizing advanced material modeling, special attention is also devoted to developing novel theories for incompressible and thermally expanding materials. A wealth of carefully chosen examples and exercises illuminate the subject matter and facilitate self-study. Uses direct notation for a clear and straightforward presentation of the mathematics, leading to a better understanding of the underlying physics Covers high-interest research areas such as small- and large-deformation continuum electrodynamics, with application to smart materials used in intelligent systems and structures Offers a unique approach to modeling incompressibility and thermal expansion, based on the authors’ own research
Euler as Physicist
Author: Dieter Suisky
Publisher: Springer Science & Business Media
Published: 2008-12-05
Total Pages: 357
ISBN-13: 3540748652
DOWNLOAD EBOOK →The subject of the book is the development of physics in the 18th century centered upon the fundamental contributions of Leonhard Euler to physics and mathematics. This is the first book devoted to Euler as a physicist. Classical mechanics are reconstructed in terms of the program initiated by Euler in 1736 and its completion over the following decades until 1760. The book examines how Euler coordinated his progress in mathematics with his progress in physics.
Exterior Differential Systems and Euler-Lagrange Partial Differential Equations
Author: Robert Bryant
Publisher: University of Chicago Press
Published: 2003-07
Total Pages: 230
ISBN-13: 9780226077932
DOWNLOAD EBOOK →In Exterior Differential Systems, the authors present the results of their ongoing development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincaré-Cartan forms. They also cover certain aspects of the theory of exterior differential systems, which provides the language and techniques for the entire study. Because it plays a central role in uncovering geometric properties of differential equations, the method of equivalence is particularly emphasized. In addition, the authors discuss conformally invariant systems at length, including results on the classification and application of symmetries and conservation laws. The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws. This timely synthesis of partial differential equations and differential geometry will be of fundamental importance to both students and experienced researchers working in geometric analysis.
Euler's Formula and Special Relativity
Author: Dr. Thomas Stark
Publisher: Magus Books
Published:
Total Pages: 175
ISBN-13:
DOWNLOAD EBOOK →What are space and time? Where do they come from? How are they possible? The answer lies in the most important and powerful equation ever discovered: Euler's Formula. This extraordinary formula is the basis of eternal existence. It furnishes the building blocks of reality. It not only explains the pre-time, pre-space domain that produces the Big Bang universe, it also solves the intractable problem of Cartesian dualism by showing exactly how mind produces matter. As we demonstrate mathematically, Euler's Formula is the true basis of Einstein's special theory of relativity, and the all-important Lorentz transformations. Euler's Formula reveals the exact difference between Einstein's relativity and Lorentz's relativity, and shows how they can be reconciled via a higher level of theory. Reality is nothing like what it seems. Do you want to know how deep the rabbit hole goes? Are you ready for the ride of your life? Are you ready to discover the true secrets of reality?
Letters of Euler on Different Subjects in Physics and Philosophy
Recent Progress in the Theory of the Euler and Navier-Stokes Equations
Author: James C. Robinson
Publisher: Cambridge University Press
Published: 2016-01-21
Total Pages: 247
ISBN-13: 1107554977
DOWNLOAD EBOOK →An accessible summary of a wide range of active research topics written by leaders in their field, including exciting new results.
