Mathematical Foundation of Turbulent Viscous Flows: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 1-5, 2003 / Edition 1

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $44.95
Usually ships in 1-2 business days
(Save 35%)
Other sellers (Paperback)
  • All (8) from $44.95   
  • New (6) from $44.95   
  • Used (2) from $109.12   
Close
Sort by
Page 1 of 1
Showing All
Note: Marketplace items are not eligible for any BN.com coupons and promotions
$44.95
Seller since 2006

Feedback rating:

(380)

Condition:

New — never opened or used in original packaging.

Like New — packaging may have been opened. A "Like New" item is suitable to give as a gift.

Very Good — may have minor signs of wear on packaging but item works perfectly and has no damage.

Good — item is in good condition but packaging may have signs of shelf wear/aging or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Acceptable — item is in working order but may show signs of wear such as scratches or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Used — An item that has been opened and may show signs of wear. All specific defects should be noted in the Comments section associated with each item.

Refurbished — A used item that has been renewed or updated and verified to be in proper working condition. Not necessarily completed by the original manufacturer.

New
PAPERBACK New 3540285865 Springer trade paperback, 2006, sealed in shrinkwrap, No marks or damage...NEW...Bubble-wrapped and mailed in a Box w/delivery confirmation.

Ships from: New Hartford, CT

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
  • Express, 48 States
  • Express (AK, HI)
$50.31
Seller since 2009

Feedback rating:

(110)

Condition: New
New Book from multilingual publisher. Shipped from UK within 4 to 14 business days. Please check language within??the description. Established seller since 2000.

Ships from: Fairford, United Kingdom

Usually ships in 1-2 business days

  • Standard, 48 States
  • Standard (AK, HI)
$51.88
Seller since 2014

Feedback rating:

(0)

Condition: New
3540285865 New Book. Please allow 4-14 business days to arrive. We will ship Internationally as well. Very Good Customer Service is Guaranteed!! Millions sold offline.

Ships from: Newport, United Kingdom

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
$51.88
Seller since 2014

Feedback rating:

(0)

Condition: New
3540285865 New Book. Please allow 4-14 business days to arrive. We will ship Internationally as well. Very Good Customer Service is Guaranteed!! Millions sold offline.

Ships from: Newport, United Kingdom

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
$54.37
Seller since 2007

Feedback rating:

(23157)

Condition: New
BRAND NEW

Ships from: Avenel, NJ

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
$66.60
Seller since 2014

Feedback rating:

(0)

Condition: New
3540285865 New Book. Please allow 4-14 business days to arrive. We will ship Internationally as well. Very Good Customer Service is Guaranteed!! Millions sold offline.

Ships from: Newport, United Kingdom

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
Page 1 of 1
Showing All
Close
Sort by

Overview

Five leading specialists reflect on different and complementary approaches to fundamental questions in the study of the Fluid Mechanics and Gas Dynamics equations. Constantin presents the Euler equations of ideal incompressible fluids and discusses the blow-up problem for the Navier-Stokes equations of viscous fluids, describing some of the major mathematical questions of turbulence theory. These questions are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations that is explained in Gallavotti's lectures. Kazhikhov introduces the theory of strong approximation of weak limits via the method of averaging, applied to Navier-Stokes equations. Y. Meyer focuses on several nonlinear evolution equations - in particular Navier-Stokes - and some related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, whenever it is localized in space or in time variable. Ukai presents the asymptotic analysis theory of fluid equations. He discusses the Cauchy-Kovalevskaya technique for the Boltzmann-Grad limit of the Newtonian equation, the multi-scale analysis, giving the compressible and incompressible limits of the Boltzmann equation, and the analysis of their initial layers.

Read More Show Less

Product Details

Table of Contents


Euler Equations, Navier-Stokes Equations and Turbulence   Peter Constantin     1
Introduction     1
Euler Equations     2
An Infinite Energy Blow Up Example     10
Navier-Stokes Equations     16
Approximations     24
The QG Equation     26
Dissipation and Spectra     30
References     39
CKN Theory of Singularities of Weak Solutions of the Navier-Stokes Equations   Giovanni Gallavotti     45
Leray's Solutions and Energy     47
Kinematic Inequalities     49
Pseudo Navier Stokes Velocity - Pressure Pairs. Scaling Operators     50
The Theorems of Scheffer and of Caffarelli-Kohn-Nirenberg     54
Fractal Dimension of Singularities of the Navier-Stokes Equation, d = 3     58
Dimension and Measure of Hausdorff     58
Hausdorff Dimension of Singular Times in the Navier-Stokes Solutions (d = 3)     59
Hausdorff Dimension in Space-Time of the Solutions of NS, (d = 3)     61
Problems. The Dimensional Bounds of the CKN Theory     63
References     73
Approximation of Weak Limits and Related Problems   Alexandre V. Kazhikhov     75
Strong Approximation of Weak Limits byAveragings     76
Notations and Basic Notions from Orlicz Function Spaces Theory     76
Strong Approximation of Weak Limits     79
Simple example     79
One-dimensional case, Steklov averaging     80
The general case     81
Remark 1.1     82
Applications to Navier-Stokes Equations     82
Transport Equations in Orlicz Spaces     83
Statement of Problem     83
Existence and Uniqueness Theorems     85
Gronwall-type Inequality and Osgood Uniqueness Theorem     86
Conclusive Remarks     88
Some Remarks on Compensated Compactness Theory     89
Introduction     89
Classical Compactness (Aubin-Simon Theorem)     91
Compensated Compactness - "div-curl" Lemma     92
Compensated Compactness-theorem of L. Tartar     94
Generalizations and Examples     96
References     98
Oscillating Patterns in Some Nonlinear Evolution Equations   Yves Meyer     101
Introduction     101
A Model Case: the Nonlinear Heat Equation     103
Navier-Stokes Equations     113
The L[superscript 2]-theory is Unstable     118
T. Kato's Theorem     124
The Kato Theorem Revisited   Marco Cannone     127
The Kato Theory with Lorentz Spaces     132
Vortex Filaments and a Theorem   Y. Giga   T. Miyakawa     136
Vortex Patches     142
The H. Koch & D. Tataru Theorem     144
Localized Velocity Fields     146
Large Time Behavior of Solutions to the Navier-Stokes Equations     151
Improved Gagliardo-Nirenberg Inequalities     154
The Space BV of Functions with Bounded Variation in the Plane     157
Gagliardo-Nirenberg Inequalities and BV     161
Improved Poincare Inequalities     166
A Direct Proof of Theorem 15.3     170
Littlewood-Paley Analysis     172
Littlewood-Paley Analysis and Wavelet Analysis     178
References     182
Asymptotic Analysis of Fluid Equations   Seiji Ukai     189
Introduction     189
Schemes for Establishing Asymptotic Relations     194
From Newton Equation to Boltzmann Equation: Boltzmann-Grad Limit     194
Newton Equation - Hard Sphere Gas     195
Liouville Equation     196
BBGKY Hierarchy     196
Boltzmann Hierarchy      198
Boltzmann Equation     198
Collision Operator Q     200
From Boltzmann Equation to Fluid Equations - Multi-Scale Analysis     202
The Case ([alpha],[Beta]) = (0,0): Compressible Euler Equation (C.E.)     204
The Case [alpha] > 0, [Beta] = 0     205
The Case [alpha] [greater than or equal] 0,[Beta] > 0     205
Abstract Cauchy-Kovalevskaya Theorem     212
Example 1: Pseudo Differential Equation     216
Example 2: Local Solutions of the Boltzmann Equation     219
The Boltzmann-Grad Limit     223
Integral Equations     223
Local Solutions and Uniform Estimates     224
Lanford's Theorem     229
Fluid Dynamical Limits     232
Preliminary     233
Main Theorems     235
Proof of Theorem 5.1     238
Proof of Theorems 5.2 and 5.3     243
References     248
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)