Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case PDF full book. Access full book title Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case by Jacob Bedrossian. Download full books in PDF and EPUB format.
Author: Jacob Bedrossian
Publisher: American Mathematical Soc.
ISBN: 1470442175
Category : Mathematics
Languages : en
Pages : 154
Get Book Here
Book Description
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.
Author: Jacob Bedrossian
Publisher: American Mathematical Soc.
ISBN: 1470442175
Category : Mathematics
Languages : en
Pages : 154
Get Book Here
Book Description
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.
Author: Jacob Bedrossian
Publisher:
ISBN: 9781470472313
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Author: Jacob Bedrossian
Publisher: American Mathematical Society
ISBN: 1470472252
Category : Mathematics
Languages : en
Pages : 148
Get Book Here
Book Description
View the abstract.
Author: Qi Chen
Publisher: American Mathematical Society
ISBN: 1470468956
Category : Mathematics
Languages : en
Pages : 190
Get Book Here
Book Description
View the abstract.
Author: Jacob Bedrossian
Publisher: American Mathematical Society
ISBN: 1470471787
Category : Mathematics
Languages : en
Pages : 235
Get Book Here
Book Description
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.
Author: S. Grivaux
Publisher: American Mathematical Soc.
ISBN: 1470446634
Category : Education
Languages : en
Pages : 147
Get Book Here
Book Description
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.
Author: Mark Pollicott
Publisher: American Mathematical Society
ISBN: 1470465779
Category : Mathematics
Languages : en
Pages : 139
Get Book Here
Book Description
View the abstract.
Author: David A. Croydon
Publisher: American Mathematical Society
ISBN: 1470456338
Category : Mathematics
Languages : en
Pages : 114
Get Book Here
Book Description
View the abstract.
Author: Matthew Bainbridge
Publisher: American Mathematical Society
ISBN: 1470455390
Category : Mathematics
Languages : en
Pages : 112
Get Book Here
Book Description
View the abstract.
Author: Jonathan Gantner
Publisher: American Mathematical Society
ISBN: 1470442388
Category : Mathematics
Languages : en
Pages : 114
Get Book Here
Book Description
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.
