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Contributions to Current Challenges in Mathematical Fluid Mechanics

This volume consists of five research articles, each dedicated to a significant topic in the mathematical theory of the Navier-Stokes equations, for compressible and incompressible fluids, and to related questions. All results given here are new and represent a noticeable contribution to the subject...

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Bibliographic Details
Other Authors: Galdi, Giovanni P. (Editor), Heywood, John G. (Editor), Rannacher, Rolf (Editor)
Format: eBook
Language:English
Published: Basel Birkhäuser 2004, 2004
Edition:1st ed. 2004
Series:Advances in Mathematical Fluid Mechanics
Subjects:
Classical And Continuum Physics
Mathematical Physics
Physics
Differential Equations
Mathematical Methods In Physics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • On Multidimensional Burgers Type Equations with Small Viscosity
  • 1. Introduction
  • 2. Upper estimates
  • 3. Lower estimates
  • 4. Fourier coefficients
  • 5. Low bounds for spatial derivatives of solutions of the Navier—Stokes system
  • References
  • On the Global Well-posedness and Stability of the Navier—Stokes and the Related Equations
  • 1. Introduction
  • 2. Littlewood—Paley decomposition
  • 3. Proof of Theorems
  • References
  • The Commutation Error of the Space Averaged Navier—Stokes Equations on a Bounded Domain
  • 1. Introduction
  • 2. The space averaged Navier-Stokes equations in a bounded domain
  • 3. The Gaussian filter
  • 4. Error estimates in the (Lp(?d))d—norm of the commutation error term
  • 5. Error estimates in the (H-1(?))d—norm of the commutation error term
  • 6. Error estimates for a weak form of the commutation error term
  • 7. The boundedness of the kinetic energy for ñ in some LES models
  • References
  • The Nonstationary Stokes and Navier—Stokes Flows Through an Aperture
  • 1. Introduction
  • 2. Results
  • 3. The Stokes resolvent for the half space
  • 4. The Stokes resolvent
  • 5. L4-Lr estimates of the Stokes semigroup
  • 6. The Navier—Stokes flow
  • References
  • Asymptotic Behavior at Infinity of Exterior Three-dimensional Steady Compressible Flow
  • 1. Introduction
  • 2. Function spaces and auxiliary results
  • 3. Stokes and modified Stokes problems in weighted spaces
  • 4. Transport equation and Poisson-type equation
  • 5. Linearized problem
  • 6. Nonlinear problem
  • References

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