Cover Image
Read Now

Fundamental Directions in Mathematical Fluid Mechanics

This volume consists of six articles, each treating an important topic in the theory ofthe Navier-Stokes equations, at the research level. Some of the articles are mainly expository, putting together, in a unified setting, the results of recent research papers and conference lectures. Several other...

Full description

Bibliographic Details
Other Authors: Galdi, Giovanni P. (Editor), Heywood, John G. (Editor), Rannacher, Rolf (Editor)
Format: eBook
Language:English
Published: Basel Birkhäuser 2000, 2000
Edition:1st ed. 2000
Series:Advances in Mathematical Fluid Mechanics
Subjects:
Classical Mechanics
Mathematical Analysis
Analysis
Mathematical Physics
Mechanics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 6 A review of theoretical analysis
  • 7 Error control and mesh adaptation
  • 8 Extension to weakly compressible flows
  • References
  • An Introduction to the Navier-Stokes Initial-Boundary Value Problem
  • 0 Introduction
  • 1 Some considerations on the structure of the Navier-Stokes equations
  • 2 The Leray-Hopf weak solutions and related properties
  • 3 Existence of weak solutions
  • 4 The energy equality and uniqueness of weak solutions
  • 5 Regularity of weak solutions
  • 6 More regular solutions and the “théorème de structure”
  • 7 Existence in the class Lr (0,T; Ls(?), 2/r +n/s = 1, and further regularity properties
  • References
  • Spectral Approximation of Navier-Stokes Equations
  • 1 Mathematical foundation and different paradigms of spectral methods
  • 2 Stokes and Navier-Stokes equations
  • 3 Time-differentiation of Navier Stokes equations
  • 4 Domain decomposition methods
  • 5 Numerical results
  • References
  • Simple Proofs of Bifurcation Theorems
  • 1 Introduction
  • 2 Bifurcation of equilibrium solutions
  • 3 Bifurcation of periodic solutions
  • 4 Generalizations
  • Appendix A: Proof of Proposition 3.1
  • References
  • On The Steady Transport Equation
  • 1 Introduction
  • 2 Existence in W1,2 ? Lq for the scalar transport equation
  • 3 Existence in W1,2 ? Lq for the scalar transport equation
  • 4 Estimates for ???2,2, ???? and ?????1,2
  • 5 Existence in Wm,2 (?), for any fixed m
  • 6 Integration along characteristics
  • References
  • On the Existence and Uniqueness Theory for the Steady Compressible Viscous Flow
  • 1 Introduction
  • 2 Poisson-Stokes equations for isothermal flow
  • 3 Main result
  • 4 Iterative scheme
  • 5 Regularity lemmas
  • 6 Bounds for the iterates
  • 7 Convergence of the iterates
  • 8 Uniqueness in the ball of existence
  • 9 Uniqueness reconsidered directly
  • References
  • Finite Element Methods for the Incompressible Navier-Stokes Equations
  • 1 Introduction
  • 2 Models of viscousflow
  • 3 Spatial discretization by finite elements
  • 4 Time discretization and linearization
  • 5 Solution of the algebraic systems

Similar Items