Dynamics Near The Subcritical Transition Of The 3d Couette Flow I Below Threshold Case
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Dynamics Near The Subcritical Transition Of The 3d Couette Flow I Below Threshold Case
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Author : Jacob Bedrossian
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Dynamics Near The Subcritical Transition Of The 3d Couette Flow I Below Threshold Case written by Jacob Bedrossian 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 2020-09-28 with Mathematics categories.
The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $epsilon leq c_0mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t rightarrow infty $. For times $t gtrsim mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of ``2.5 dimensional'' streamwise-independent solutions referred to as streaks.
Dynamics Near The Subcritical Transition Of The 3d Couette Flow Ii Above Threshold Case
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Author : Jacob Bedrossian
language : en
Publisher: American Mathematical Society
Release Date : 2022-08-31
Dynamics Near The Subcritical Transition Of The 3d Couette Flow Ii Above Threshold Case written by Jacob Bedrossian 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 2022-08-31 with Mathematics categories.
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Transition Threshold For The 3d Couette Flow In A Finite Channel
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Author : Qi Chen
language : en
Publisher: American Mathematical Society
Release Date : 2024-05-15
Transition Threshold For The 3d Couette Flow In A Finite Channel written by Qi Chen 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 2024-05-15 with Mathematics categories.
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The Mathematical Analysis Of The Incompressible Euler And Navier Stokes Equations
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Author : Jacob Bedrossian
language : en
Publisher: American Mathematical Society
Release Date : 2022-09-22
The Mathematical Analysis Of The Incompressible Euler And Navier Stokes Equations written by Jacob Bedrossian 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 2022-09-22 with Mathematics categories.
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.
Asymptotic Counting In Conformal Dynamical Systems
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Author : Mark Pollicott
language : en
Publisher: American Mathematical Society
Release Date : 2021-09-24
Asymptotic Counting In Conformal Dynamical Systems written by Mark Pollicott 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 2021-09-24 with Mathematics categories.
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Linear Dynamical Systems On Hilbert Spaces Typical Properties And Explicit Examples
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Author : S. Grivaux
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Linear Dynamical Systems On Hilbert Spaces Typical Properties And Explicit Examples written by S. Grivaux 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 2021-06-21 with Education categories.
We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. (i) A typical hypercyclic operator is not topologically mixing, has no eigen-values and admits no non-trivial invariant measure, but is densely distri-butionally chaotic. (ii) A typical upper-triangular operator with coefficients of modulus 1 on the diagonal is ergodic in the Gaussian sense, whereas a typical operator of the form “diagonal with coefficients of modulus 1 on the diagonal plus backward unilateral weighted shift” is ergodic but has only countably many unimodular eigenvalues; in particular, it is ergodic but not ergodic in the Gaussian sense. (iii) There exist Hilbert space operators which are chaotic and U-frequently hypercyclic but not frequently hypercyclic, Hilbert space operators which are chaotic and frequently hypercyclic but not ergodic, and Hilbert space operators which are chaotic and topologically mixing but not U-frequently hypercyclic. We complement our results by investigating the descriptive complexity of some natural classes of operators defined by dynamical properties.
Resolvent Heat Kernel And Torsion Under Degeneration To Fibered Cusps
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Author : Pierre Albin
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Resolvent Heat Kernel And Torsion Under Degeneration To Fibered Cusps written by Pierre Albin 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 2021-06-21 with Education categories.
Manifolds with fibered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary.
Operator Theory On One Sided Quaternion Linear Spaces Intrinsic S Functional Calculus And Spectral Operators
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Author : Jonathan Gantner
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Operator Theory On One Sided Quaternion Linear Spaces Intrinsic S Functional Calculus And Spectral Operators written by Jonathan Gantner 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 2021-02-10 with Mathematics categories.
Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space $V$. This has technical reasons, as the space of bounded operators on $V$ is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.
Ojasiewicz Simon Gradient Inequalities For Coupled Yang Mills Energy Functionals
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Author : Paul M Feehan
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Ojasiewicz Simon Gradient Inequalities For Coupled Yang Mills Energy Functionals written by Paul M Feehan 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 2021-02-10 with Mathematics categories.
The authors' primary goal in this monograph is to prove Łojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces that impose minimal regularity requirements on pairs of connections and sections.
Theory Of Fundamental Bessel Functions Of High Rank
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Author : Zhi Qi
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Theory Of Fundamental Bessel Functions Of High Rank written by Zhi Qi 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 2021-02-10 with Mathematics categories.
In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.