The Partial Regularity Theory Of Caffarelli Kohn And Nirenberg And Its Sharpness
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The Partial Regularity Theory Of Caffarelli Kohn And Nirenberg And Its Sharpness
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Author : Wojciech S. Ożański
language : en
Publisher: Springer Nature
Release Date : 2019-09-16
The Partial Regularity Theory Of Caffarelli Kohn And Nirenberg And Its Sharpness written by Wojciech S. Ożański and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-16 with Mathematics categories.
This monograph focuses on the partial regularity theorem, as developed by Caffarelli, Kohn, and Nirenberg (CKN), and offers a proof of the upper bound on the Hausdorff dimension of the singular set of weak solutions of the Navier-Stokes inequality, while also providing a clear and insightful presentation of Scheffer’s constructions showing their bound cannot be improved. A short, complete, and self-contained proof of CKN is presented in the second chapter, allowing the remainder of the book to be fully dedicated to a topic of central importance: the sharpness result of Scheffer. Chapters three and four contain a highly readable proof of this result, featuring new improvements as well. Researchers in mathematical fluid mechanics, as well as those working in partial differential equations more generally, will find this monograph invaluable.
Mathematical Analysis Of The Navier Stokes Equations
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Author : Matthias Hieber
language : en
Publisher: Springer Nature
Release Date : 2020-04-28
Mathematical Analysis Of The Navier Stokes Equations written by Matthias Hieber and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-28 with Mathematics categories.
This book collects together a unique set of articles dedicated to several fundamental aspects of the Navier–Stokes equations. As is well known, understanding the mathematical properties of these equations, along with their physical interpretation, constitutes one of the most challenging questions of applied mathematics. Indeed, the Navier-Stokes equations feature among the Clay Mathematics Institute's seven Millennium Prize Problems (existence of global in time, regular solutions corresponding to initial data of unrestricted magnitude). The text comprises three extensive contributions covering the following topics: (1) Operator-Valued H∞-calculus, R-boundedness, Fourier multipliers and maximal Lp-regularity theory for a large, abstract class of quasi-linear evolution problems with applications to Navier–Stokes equations and other fluid model equations; (2) Classical existence, uniqueness and regularity theorems of solutions to the Navier–Stokes initial-value problem, along with space-time partial regularity and investigation of the smoothness of the Lagrangean flow map; and (3) A complete mathematical theory of R-boundedness and maximal regularity with applications to free boundary problems for the Navier–Stokes equations with and without surface tension. Offering a general mathematical framework that could be used to study fluid problems and, more generally, a wide class of abstract evolution equations, this volume is aimed at graduate students and researchers who want to become acquainted with fundamental problems related to the Navier–Stokes equations.
Proceedings Of The St Petersburg Mathematical Society Volume Xv
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Author : Darya Apushkinskaya
language : en
Publisher: American Mathematical Society
Release Date : 2014-08-22
Proceedings Of The St Petersburg Mathematical Society Volume Xv written by Darya Apushkinskaya and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-22 with Mathematics categories.
This book presents the proceedings of the international workshop, "Advances in Mathematical Analysis of Partial Differential Equations" held at the Institut Mittag-Leffler, Stockholm, Sweden, July 9-13, 2012, dedicated to the memory of the outstanding Russian mathematician Olga A. Ladyzhenskaya. The volume contains papers that engage a wide set of modern topics in the theory of linear and nonlinear partial differential equations and applications, including variational and free boundary problems, mathematical problems of hydrodynamics, and magneto-geostrophic equations.
Numerical Mathematics And Advanced Applications
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Author : Alfredo Bermúdez de Castro
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-08
Numerical Mathematics And Advanced Applications written by Alfredo Bermúdez de Castro and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-08 with Mathematics categories.
These proceedings collect lectures given at ENUMATH 2005, the 6th European Conference on Numerical Mathematics and Advanced Applications held in Santiago de Compostela, Spain in July, 2005. Topics include applications such as fluid dynamics, electromagnetism, structural mechanics, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, and more.
Mathematical Analysis In Fluid Mechanics
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Author : Raphaël Danchin
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-06-26
Mathematical Analysis In Fluid Mechanics written by Raphaël Danchin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-26 with Mathematics categories.
This volume contains the proceedings of the International Conference on Vorticity, Rotation and Symmetry (IV)—Complex Fluids and the Issue of Regularity, held from May 8–12, 2017, in Luminy, Marseille, France. The papers cover topics in mathematical fluid mechanics ranging from the classical regularity issue for solutions of the 3D Navier-Stokes system to compressible and non-Newtonian fluids, MHD flows and mixtures of fluids. Topics of different kinds of solutions, boundary conditions, and interfaces are also discussed.
The Abel Prize 2013 2017
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Author : Helge Holden
language : en
Publisher: Springer
Release Date : 2019-02-23
The Abel Prize 2013 2017 written by Helge Holden and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-23 with Mathematics categories.
The book presents the winners of the Abel Prize in mathematics for the period 2013–17: Pierre Deligne (2013); Yakov G. Sinai (2014); John Nash Jr. and Louis Nirenberg (2015); Sir Andrew Wiles (2016); and Yves Meyer (2017). The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee. The book also includes photos for the period 2003–2017 showing many of the additional activities connected with the Abel Prize. As an added feature, video interviews with the Laureates as well as videos from the prize ceremony are provided at an accompanying website (http://extras.springer.com/). This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer 2014), which profile the work of the previous Abel Prize winners.
Numerical Analysis Of Dissipative Dynamical Systems In Solid And Fluid Mechanics With A Special Emphasis On Coupled Problems
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Author : Stanford University. Division of Applied Mechanics. Division of Applied Mechanics
language : en
Publisher:
Release Date : 1993
Numerical Analysis Of Dissipative Dynamical Systems In Solid And Fluid Mechanics With A Special Emphasis On Coupled Problems written by Stanford University. Division of Applied Mechanics. Division of Applied Mechanics and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2008
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The Navier Stokes Problem In The 21st Century
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Author : Pierre Gilles Lemarie-Rieusset
language : en
Publisher: CRC Press
Release Date : 2016-04-06
The Navier Stokes Problem In The 21st Century written by Pierre Gilles Lemarie-Rieusset and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-06 with Mathematics categories.
Up-to-Date Coverage of the Navier–Stokes Equation from an Expert in Harmonic Analysis The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier–Stokes Problem in the 21st Century provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics. The book focuses on incompressible deterministic Navier–Stokes equations in the case of a fluid filling the whole space. It explores the meaning of the equations, open problems, and recent progress. It includes classical results on local existence and studies criterion for regularity or uniqueness of solutions. The book also incorporates historical references to the (pre)history of the equations as well as recent references that highlight active mathematical research in the field.
Singular Limits In Thermodynamics Of Viscous Fluids
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Author : Eduard Feireisl
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-28
Singular Limits In Thermodynamics Of Viscous Fluids written by Eduard Feireisl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-28 with Science categories.
Many interesting problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations as certain parameters vanish or become infinite. Frequently the limiting solution, provided the limit exists, satisfies a qualitatively different system of differential equations. This book is designed as an introduction to the problems involving singular limits based on the concept of weak or variational solutions. The primitive system consists of a complete system of partial differential equations describing the time evolution of the three basic state variables: the density, the velocity, and the absolute temperature associated to a fluid, which is supposed to be compressible, viscous, and heat conducting. It can be represented by the Navier-Stokes-Fourier-system that combines Newton's rheological law for the viscous stress and Fourier's law of heat conduction for the internal energy flux. As a summary, this book studies singular limits of weak solutions to the system governing the flow of thermally conducting compressible viscous fluids.