Author 
Mak, Ronald, 1953

Subject 
Mars Exploration Rover Mission (U.S.)  Data processing.


Computer systems  Design  Case studies.


Business  Data processing  Case studies.


Roving vehicles (Astronautics)  Automatic control  Data processing.


Mars (Planet)  Exploration  Data processing.

Alt Name 
Mars Exploration Rover Mission (U.S.)

Description 
1 online resource (xxx, 138 pages) : illustrations 
Note 
Includes index. 
Contents 
Cover Contents Preface Acknowledgments I Introduction and Overview of Turbulence Introduction 1 Viscous Fluids. The Navier Stokes Equations Nondimensional Form of the Navier Stokes Equations 2 Turbulence: Where the Interests of Engineers and Mathematicians Overlap 3 Elements of the Theories of Turbulence of Kolmogorov and Kraichnan 4 Function Spaces, Functional Inequalities, and Dimensional Analysis The Fundamental Function Spaces Functional Inequalities More Inequalities Lebesgue Spaces HigherOrder Sobolev Spaces Sobolev Embeddings and Inequalities Compact Mappings, the Rellich Lemma, and Compact Sobolev Embeddings II Elements of the Mathematical Theory of the Navier Stokes Equations Introduction 1 Energy and Enstrophy 2 Boundary Value Problems NoSlip Boundary Condition SpacePeriodic Case Channel Flows Initial Condition Simplified Problems A Boundary Value Problem for the Pressure An Evolution Equation for the Velocity Field u 3 Helmholtz Leray Decomposition of Vector Fields The Evolution Equation for the Velocity Field 4 Weak Formulation of the Navier Stokes Equations Energy Equation 5 Function Spaces NoSlip Boundary Conditions Periodic Boundary Conditions Periodic Boundary Conditions with Zero Space Average Fourier Characterization of the Function Spaces for Periodic Flows Space Time Function Spaces 6 The Stokes Operator The Stokes Operator in the NoSlip Case The Stokes Operator in the SpacePeriodic Case with Vanishing Space Average The Stokes Operator in the General Periodic Case Alternative (Abstract) Definition of the Stokes Operator Asymptotic Behavior of the Eigenvalues of the Stokes Operator Galerkin (Spectral) Projectors 7 Existence and Uniqueness of Solutions: The Main Results Existence and Uniqueness in Dimension 3 Existence and Uniqueness in Dimension 2 Further Properties of the Solutions in Dimension 3 8 Analyticity in Time Time Analyticity in the 3Dimensional Case Global Analyticity in the 2Dimensional Case Improvements in the 2Dimensional Periodic Case 9 Gevrey Class Regularity and the Decay of the Fourier Coefficients Gevrey Spaces Estimates for the Nonlinear Term in the Periodic Case Analyticity in the 3Dimensional Periodic Case Analyticity in the 2Dimensional Periodic Case Exponential Decrease of the Fourier Coefficients 10 Function Spaces for the WholeSpace Case 11 The NoSlip Case with Moving Boundaries 12 Dissipation Rate of Flows Bounds on the Energy Dissipation for a 3Dimensional Shear Flow Bounds on the Energy Dissipation for Periodic Flows 13 Nondimensional Estimates and the Grashof Number The 2Dimensional Case The 3Dimensional Case Appendix A Mathematical Complements A.1 Function Spaces A.2 Weak and Strong Solutions of the NSE in Dimension 3 A.3 Weak and Strong Solutions of the NSE in Dimension 2 Appendix B Proofs of Technical Results in Chapter II B.1 Energy Equation and A Priori Estimates B.2 Time Analyticity B.3 Bilinear Estimates in Gevrey Spaces B.4 Time Analyticity in Gevrey Spaces III Finite Dimensionality of Flows Introduction Elements of the Mathematical Theory of the NSE 1 Determining Modes Determining Modes in the NoSlip Case Determining Modes in the SpacePeriodic Case 2 Determining Nodes Determining Nodes in the NoSlip Case Determining Nodes in the SpacePeriodic Case 3 Attractors and Their Fractal Dimension 3.1 The Global Attractor for the 2Dimensional Navier Stokes Equations 3.2 The 3Dimensional Navier Stokes Equations 4 Approximate Inertial Manifolds Appendix A Proofs of Technical Results in Chapter III A.1 Proof of the Generalized Gronwall Lemma 1.1 A.2 Proof of Lemma 2.1 A.3 Estimates for the Dimension of the Global Attractor A.4 Proof of the Triviality of the Attractor with Force in the First Mode A.5 Attraction and Compactness of the 3Dimensional Weak Global Attractor A.6 Error Bounds for the FMT Approximate In. 
ISBN 
0471789658 (pbk.) 

9780471789659 

0470046317 (electronic bk.) 

9780470046319 (electronic bk.) 

6610447764 

9786610447763 
OCLC # 
69314332 
Additional Format 
Print version: Mak, Ronald, 1953 Martian principles for successful enterprise systems. Indianapolis, IN : Wiley Pub., ©2006 0471789658 (DLC) 2006003347 (OCoLC)63692578. 
