Attractors representing turbulent flows / P. Constantin, C. Foiaş, and R. Temam.

Format:

Book

Author/Creator:

Constantin, P. (Peter), 1951- author.

Foiaş, Ciprian, author.

Temam, Roger, author.

Series:

Memoirs of the American Mathematical Society ; Volume 53, Number 314.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 53, Number 314

Language:

English

Subjects (All):

Turbulence.

Navier-Stokes equations.

Physical Description:

1 online resource (79 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island, United States : American Mathematical Society, 1985.

Language Note:

English

Contents:

""TABLE OF CONTENTS""; ""INTRODUCTION""; ""CHAPTER 1 � ON THE APPEARANCE OF SINGULARITIES IN A THREE DIMENSIONAL FLOW""; ""1.1. The functional setting of the Navier-Stokes Equations""; ""1.2. The initial value problem""; ""1.3. The main resul (of Chapter 1)""; ""CHAPTER 2 � THE SQUEEZING PROPERTY FOR THE TRAJECTORIES""; ""2.1. Quotient of norms""; ""2.2. The squeezing property""; ""2.3. An application of the squeezing : image of a ball""; ""CHAPTER 3 � HAUSDORFF AND FRACTAL DIMENSIONS OF AN ATTRACTOR""; ""3.1. The Hausdorff dimension""; ""3.2. Covering Lemmas""

""3.3. Proof of Theorem 3.1""""3.4. The fractal dimension""; ""3.5. Lyapunov exponents and Lyapunov numbers""; ""3.6. Application to evolution equations""; ""CHAPTER 4 � NUMBER OF DEGREES OF FREEDOM OF A THREE DIMENSIONAL FLOW""; ""4.1. Attractors for three dimensional flows""; ""4.2. Estimate of the fractal dimension of an attractor""; ""4.3. Explicit values of the bound of the dimension""; ""4.3.a. Estimate of the number of degrees of freedom in term of the Kolmogorov dissipation length""; ""4.3.b. Estimate in term of a Reynolds number""; ""4.3.c. Another Reynold number""

""4.3.d. A Reynold number based on the enstrophy""""4.4. Other aspects of the finite dimensionality of 3-D turbulent flows""; ""4.5. Consequences of the Lieb-Thirring's inequality""; ""REFERENCES""

Notes:

"January 1985, Volume 53, Number 314 (first of 5 numbers)"--Cover.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0727-2