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Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case
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 $\\epsilon \\leq c_0\\mathbf {Re}^-1$ 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.
eBook
Global Smooth Solutions for the Inviscid SQG Equation
In this paper, we show the existence of the first non trivial family of classical global solutions of the inviscid surface
quasi-geostrophic equation.
eBook
Dynamics Near the Subcritical Transition of the 3D Couette Flow II: Above Threshold Case
This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible
Navier-Stokes equations at high Reynolds number
eBook
Thermodynamics : concepts and applications
\"Thermodynamics is one of three disciplines known collectively as the thermal-fluid sciences, sometimes just the thermal sciences: thermodynamics, heat transfer, and fluid mechanics. We begin with a dictionary definition of thermodynamics.\"-- Provided by publisher.
BOOK
Quasi-Periodic Standing Wave Solutions of Gravity-Capillary Water Waves
The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
eBook
Fundamental mechanics of fluids
\"Fully updated and expanded to reflect the staggering advances in modern mathematics, this fourth edition boasts 40 new homework problems (nearly 150 in total); new appendix material summarizing vectors, tensors, complex variables, and governing equations in common coordinate systems; and a new chapter on similarity solutions, group invariance solutions, separation of variables solutions, and some Fourier series representations. Illustrating basic equations and strategies to analyze fluid dynamics, mechanisms, and behavior, this new edition also contains reworked line drawings, revised problems, and extended end-of-chapter questions for clarification and expansion of key concepts\"-- Provided by publisher.
Book
On Singular Vortex Patches, I: Well-posedness Issues
The purpose of this work is to discuss the well-posedness theory of singular vortex patches. Our main results are of two types:
well-posedness and ill-posedness. On the well-posedness side, we show that globally
eBook