03197nam 2200589 450 991078888880332120170821172555.01-4704-0727-2(CKB)3360000000464498(EBL)3113905(SSID)ssj0000888780(PQKBManifestationID)11465738(PQKBTitleCode)TC0000888780(PQKBWorkID)10865782(PQKB)10909006(MiAaPQ)EBC3113905(RPAM)4260608(PPN)195411951(EXLCZ)99336000000046449820140903h19851985 uy 0engur|n|---|||||txtccrAttractors representing turbulent flows /P. Constantin, C. Foiaş, and R. TemamProvidence, Rhode Island, United States :American Mathematical Society,1985.©19851 online resource (79 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 53, Number 314"January 1985, Volume 53, Number 314 (first of 5 numbers)"--Cover.0-8218-2315-9 Includes bibliographical references.""TABLE OF CONTENTS""; ""INTRODUCTION""; ""CHAPTER 1 â€? 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 â€? 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 â€? 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 â€? 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""Memoirs of the American Mathematical Society ;Volume 53, Number 314.TurbulenceNavier-Stokes equationsTurbulence.Navier-Stokes equations.532/.0527Constantin P(Peter),1951-1545046Foiaş CiprianTemam RogerMiAaPQMiAaPQMiAaPQBOOK9910788888803321Attractors representing turbulent flows3799681UNINA