Keywords:
Navier-Stokes equations-Congresses.
;
Electronic books.
Type of Medium:
Online Resource
Pages:
1 online resource (265 pages)
Edition:
1st ed.
ISBN:
9783540324546
Series Statement:
Lecture Notes in Mathematics Series ; v.1871
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=5591204
DDC:
532/.58
Language:
English
Note:
Intro -- Euler Equations, Navier-Stokes Equations and Turbulence -- Peter Constantin -- 1 Introduction -- 2 Euler Equations -- 3 An Infinite Energy Blow Up Example -- 4 Navier-Stokes Equations -- 5 Approximations -- 6 The QG Equation -- 7 Dissipation and Spectra -- References -- CKN Theory of Singularities of Weak Solutions of the Navier-Stokes Equations -- Giovanni Gallavotti -- 1 Leray's Solutions and Energy -- 2 Kinematic Inequalities -- 3 Pseudo Navier Stokes Velocity -- Pressure Pairs. Scaling Operators -- 4 The Theorems of Scheffer and of Caffarelli--Kohn--Nirenberg -- 5 Fractal Dimension of Singularitiesof the Navier--Stokes Equation, d=3 -- 5.1 Dimension and Measure of Hausdorff -- 5.2 Hausdorff Dimension of Singular Times in the Navier--Stokes Solutions (d=3) -- 5.3 Hausdorff Dimension in Space--Time of the Solutions of NS, (d=3) -- 6 Problems. The Dimensional Bounds of the CKN Theory -- References -- Approximation of Weak Limits and Related Problems -- Alexandre V. Kazhikhov -- 1 Strong Approximation of Weak Limits by Averagings -- 1.1 Notations and Basic Notions from Orlicz Function Spaces Theory -- 1.2 Strong Approximation of Weak Limits -- Step 1. Simple example. -- Step 2. One-dimensional case, Steklov averaging. -- Step 3. The general case. -- Remark 1.1 -- 1.3 Applications to Navier-Stokes Equations -- 2 Transport Equations in Orlicz Spaces -- 2.1 Statement of Problem -- 2.2 Existence and Uniqueness Theorems -- 2.3 Gronwall-type Inequality and Osgood Uniqueness Theorem -- 2.4 Conclusive Remarks -- 3 Some Remarks on Compensated Compactness Theory -- 3.1 Introduction -- 3.2 Classical Compactness (Aubin-Simon Theorem) -- 3.3 Compensated Compactness -- ``div-curl" Lemma -- 3.4 Compensated Compactness-theorem of L. Tartar -- 3.5 Generalizations and Examples -- References -- Oscillating Patterns in Some Nonlinear Evolution Equations.
,
Yves Meyer -- 1 Introduction -- 2 A Model Case: the Nonlinear Heat Equation -- 3 Navier-Stokes Equations -- 4 The L2-theory is Unstable -- 5 T. Kato's Theorem -- 6 The Kato Theorem Revisited by Marco Cannone -- 7 The Kato Theory with Lorentz Spaces -- 8 Vortex Filaments and a Theorem by Y. Giga and T. Miyakawa -- 9 Vortex Patches -- 10 The H. Koch & -- D. Tataru Theorem -- 11 Localized Velocity Fields -- 12 Large Time Behavior of Solutions to the Navier-Stokes Equations -- 13 Improved Gagliardo-Nirenberg Inequalities -- 14 The Space BV of Functions with Bounded Variation in the Plane -- 15 Gagliardo-Nirenberg Inequalities and BV -- 16 Improved Poincaré Inequalities -- 17 A Direct Proof of Theorem 15.3 -- 18 Littlewood-Paley Analysis -- 19 Littlewood-Paley Analysis and Wavelet Analysis -- References -- Asymptotic Analysis of Fluid Equations -- Seiji Ukai -- 1 Introduction -- 2 Schemes for Establishing Asymptotic Relations -- 2.1 From Newton Equation to Boltzmann Equation: Boltzmann--Grad Limit -- Newton Equation -- Hard Sphere Gas -- Liouville Equation -- BBGKY Hierarchy -- Boltzmann Hierarchy -- Boltzmann Equation -- Collision Operator Q -- 2.2 From Boltzmann Equation to Fluid Equations --Multi-Scale Analysis -- The Case (,)=(0,0): Compressible Euler Equation (C.E.) -- The Case > -- 0, =0 -- The Case 0, > -- 0 -- 3 Abstract Cauchy-Kovalevskaya Theorem -- 3.1 Example 1: Pseudo Differential Equation -- 3.2 Example 2: Local Solutions of the Boltzmann Equation -- 4 The Boltzmann-Grad Limit -- 4.1 Integral Equations -- 4.2 Local Solutions and Uniform Estimates -- 4.3 Lanford's Theorem -- 5 Fluid Dynamical Limits -- 5.1 Preliminary -- 5.2 Main Theorems -- 5.3 Proof of Theorem 5.1 -- 5.4 Proof of Theorems 5.2 and 5.3 -- References.
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