This book is a unique collection of high-level papers devoted to fundamental topics in mathematical fluid mechanics and their applications, mostly in connection with the scientific work of Giovanni Paolo Galdi. The contributions are mainly centered on the study of the basic properties of the Navier-Stokes equations, including existence, uniqueness, regularity, and stability of solutions. Related models describing non-Newtonian flows, turbulence, and fluid-structure interactions are also addressed. The results are analytical, numerical and experimental in nature, making the book particularly appealing to a vast readership encompassing mathematicians, engineers and physicists. The diversity of the topics, in addition to the different approaches, will provide readers a global and up-to-date overview of both the latest findings on the subject and of the salient open questions.
Author(s): Chérif Amrouche, Ulrich Razafison (auth.), Rolf Rannacher, Adélia Sequeira (eds.)
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2010
Language: English
Pages: 657
Tags: Applications of Mathematics;Classical Continuum Physics;Computational Mathematics and Numerical Analysis;Numerical Analysis;Biomedical Engineering
Front Matter....Pages i-xxv
Isotropically and Anisotropically Weighted Sobolev Spaces for the Oseen Equation....Pages 1-24
A New Model of Diphasic Fluids in Thin Films....Pages 25-35
On the Global Integrability for Any Finite Power of the Full Gradient for a Class of Generalized Power Law Models p < 2....Pages 37-42
Steady Flow Around a Floating Body: The Rotationally Symmetric Case....Pages 43-54
On a Stochastic Approach to Eddy Viscosity Models for Turbulent Flows....Pages 55-81
Numerical Study of the Significance of the Non-Newtonian Nature of Blood in Steady Flow Through a Stenosed Vessel....Pages 83-104
A Priori Convergence Estimates for a Rough Poisson-Dirichlet Problem with Natural Vertical Boundary Conditions....Pages 105-134
Vortex Induced Oscillations of Cylinders at Low and Intermediate Reynolds Numbers....Pages 135-145
One-dimensional Modelling of Venous Pathologies: Finite Volume and WENO Schemes....Pages 147-170
On the Energy Equality for Weak Solutions of the 3D Navier-Stokes Equations....Pages 171-175
The ( p - q ) Coupled Fluid-Energy Systems....Pages 177-190
A Potential-Theoretic Approach to the Time-Dependent Oseen System....Pages 191-214
Regularity of Weak Solutions for the Navier-Stokes Equations Via Energy Criteria....Pages 215-227
Looking for the Lost Memory in Diffusion-Reaction Equations....Pages 229-251
Maximum Principle and Gradient Estimates for Stationary Solutions of the Navier-Stokes Equations: A Partly Numerical Investigation....Pages 253-269
A Study of Shark Skin and Its Drag Reducing Mechanism....Pages 271-285
Stability of Poiseuille Flow in a Porous Medium....Pages 287-293
Towards a Geometrical Multiscale Approach to Non-Newtonian Blood Flow Simulations....Pages 295-309
The Role of Potential Flow in the Theory of the Navier-Stokes Equations....Pages 311-317
Small Perturbations of Initial Conditions of Solutions of the Navier–Stokes Equations in the L 3 –Norm and Applications....Pages 319-328
Streaming Flow Effects in the Nearly Inviscid Faraday Instability....Pages 329-338
The Dirichlet Problems for Steady Navier-Stokes Equations in Domains with Thin Channels....Pages 339-366
Existence of Weak Solutions to the Equations of Natural Convection with Dissipative Heating....Pages 367-384
A Weak Solvability of the Navier-Stokes Equation with Navier’s Boundary Condition Around a Ball Striking theWall....Pages 385-407
On the Influence of an Absorption Term in Incompressible Fluid Flows....Pages 409-424
Adaptive FE Eigenvalue Computation with Applications to Hydrodynamic Stability....Pages 425-450
Numerical Simulation of Laminar Incompressible Fluid-Structure Interaction for Elastic Material with Point Constraints....Pages 451-472
On Stokes' Problem....Pages 473-511
On a C 0 Semigroup Associated with a Modified Oseen Equation with Rotating Effect....Pages 513-551
A New Approach to the Regularity ofWeak Lq-Solutions of Stokes and Similar Equations via the Cosserat Operator....Pages 553-572
Large Time Behavior of Energy in Some Slowly Decreasing Solutions of the Navier-Stokes Equations....Pages 573-580
A Selected Survey of the Mathematical Theory of 1D Flows....Pages 581-587
A Numerical Method for Nonstationary Stokes Flow....Pages 589-611
A New Criterion for Partial Regularity of Suitable Weak Solutions to the Navier-Stokes Equations....Pages 613-630
An In Vitro Device for Evaluation of Cellular Response to Flows Found at the Apex of Arterial Bifurcations....Pages 631-657
