Author: Jacob BedrossianPublisher: American Mathematical Society
ISBN: 1470472252
Category : Mathematics
Languages : en
Pages : 148
Book Description
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Dynamics Near the Subcritical Transition of the 3D Couette Flow II: Above Threshold Case
Author: Jacob BedrossianPublisher: American Mathematical Society
ISBN: 1470472252
Category : Mathematics
Languages : en
Pages : 148
Book Description
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Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case
Author: Jacob BedrossianPublisher: American Mathematical Soc.
ISBN: 1470442175
Category : Mathematics
Languages : en
Pages : 154
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.
Transition Threshold for the 3D Couette Flow in a Finite Channel
Author: Qi ChenPublisher: American Mathematical Society
ISBN: 1470468956
Category : Mathematics
Languages : en
Pages : 190
Book Description
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The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations
Author: Jacob BedrossianPublisher: American Mathematical Society
ISBN: 1470471787
Category : Mathematics
Languages : en
Pages : 235
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.
Dynamics of the Box-Ball System with Random Initial Conditions via Pitman’s Transformation
Author: David A. CroydonPublisher: American Mathematical Society
ISBN: 1470456338
Category : Mathematics
Languages : en
Pages : 114
Book Description
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The Second Moment Theory of Families of $L$-Functions–The Case of Twisted Hecke $L$-Functions
Author: Valentin BlomerPublisher: American Mathematical Society
ISBN: 1470456788
Category : Mathematics
Languages : en
Pages : 160
Book Description
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Horocycle Dynamics: New Invariants and Eigenform Loci in the Stratum $mathcal {H}(1,1)$
Author: Matthew BainbridgePublisher: American Mathematical Society
ISBN: 1470455390
Category : Mathematics
Languages : en
Pages : 112
Book Description
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Hypergeometric Functions Over Finite Fields
Author: Jenny FuselierPublisher: American Mathematical Society
ISBN: 1470454335
Category : Mathematics
Languages : en
Pages : 138
Book Description
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The $mathscr {P}(varphi )_2$ Model on de Sitter Space
Author: João C. A. BarataPublisher: American Mathematical Society
ISBN: 147045548X
Category : Mathematics
Languages : en
Pages : 282
Book Description
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Spectral Properties of Ruelle Transfer Operators for Regular Gibbs Measures and Decay of Correlations for Contact Anosov Flows
Author: Luchezar StoyanovPublisher: American Mathematical Society
ISBN: 1470456257
Category : Mathematics
Languages : en
Pages : 134
Book Description
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