Advances in Mathematical Fluid Mechanics

Mathematical advances in fluid mechanics are presented in this informative review. The properties of Navier-Stokes equations are discussed, in addition to related models that describe non-Newtonian flows, turbulence, and fluid structure interactions.

The present volume celebrates the 60th birthday of Professor Giovanni Paolo Galdi and honors his remarkable contributions to research in the ?eld of Mathematical Fluid Mechanics. The book contains a collection of 35 peer reviewed papers, with authors from 20 countries, re?ecting the worldwide impact and great inspiration by his work over the years. These papers were selected from invited lectures and contributed talks presented at the International Conference on Mathematical Fluid Mechanics held in Estoril, Portugal, May 2125, 2007 and organized on the oc- sion of Professor Galdi's 60th birthday. We express our gratitude to all the authors and reviewers for their important contributions. Professor Galdi devotes his career to research on the mathematical analysis of the Navier-Stokes equations and non-Newtonian ?ow problems, with special emphasis on hydrodynamic stability and ?uid-particle interactions, impressing the worldwide mathematical communities with his results. His numerous contributions have laid down signi?cant milestones in these ?elds, with a great in?uence on interdis- plinary research communities. He has advanced the careers of numerous young researchers through his generosity and encouragement, some directly through int- lectual guidance and others indirectly by pairing them with well chosen senior c- laborators. A brief review of Professor Galdi's activities and some impressions by colleagues and friends are included here.

Includes supplementary material: sn.pub/extras

Texte du rabat

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.

Contenu
Isotropically and Anisotropically Weighted Sobolev Spaces for the Oseen Equation.- A New Model of Diphasic Fluids in Thin Films.- On the Global Integrability for Any Finite Power of the Full Gradient for a Class of Generalized Power Law Models #x003C; 2.- Steady Flow Around a Floating Body: The Rotationally Symmetric Case.- On a Stochastic Approach to Eddy Viscosity Models for Turbulent Flows.- Numerical Study of the Significance of the Non-Newtonian Nature of Blood in Steady Flow Through a Stenosed Vessel.- A Priori Convergence Estimates for a Rough Poisson-Dirichlet Problem with Natural Vertical Boundary Conditions.- Vortex Induced Oscillations of Cylinders at Low and Intermediate Reynolds Numbers.- One-dimensional Modelling of Venous Pathologies: Finite Volume and WENO Schemes.- On the Energy Equality for Weak Solutions of the 3D Navier-Stokes Equations.- The ( #x002D; ) Coupled Fluid-Energy Systems.- A Potential-Theoretic Approach to the Time-Dependent Oseen System.- Regularity of Weak Solutions for the Navier-Stokes Equations Via Energy Criteria.- Looking for the Lost Memory in Diffusion-Reaction Equations.- Maximum Principle and Gradient Estimates for Stationary Solutions of the Navier-Stokes Equations: A Partly Numerical Investigation.- A Study of Shark Skin and Its Drag Reducing Mechanism.- Stability of Poiseuille Flow in a Porous Medium.- Towards a Geometrical Multiscale Approach to Non-Newtonian Blood Flow Simulations.- The Role of Potential Flow in the Theory of the Navier-Stokes Equations.- Small Perturbations of Initial Conditions of Solutions of the Navier#x2013;Stokes Equations in the L#x2013;Norm and Applications.- Streaming Flow Effects in the Nearly Inviscid Faraday Instability.- The Dirichlet Problems for Steady Navier-Stokes Equations in Domains with Thin Channels.- Existence of Weak Solutions to the Equations of Natural Convection with Dissipative Heating.- A Weak Solvability of the Navier-Stokes Equation with Navier#x2019;s Boundary Condition Around a Ball Striking theWall.- On the Influence of an Absorption Term in Incompressible Fluid Flows.- Adaptive FE Eigenvalue Computation with Applications to Hydrodynamic Stability.- Numerical Simulation of Laminar Incompressible Fluid-Structure Interaction for Elastic Material with Point Constraints.- On Stokes#x0027; Problem.- On a Semigroup Associated with a Modified Oseen Equation with Rotating Effect.- A New Approach to the Regularity ofWeak Lq-Solutions of Stokes and Similar Equations via the Cosserat Operator.- Large Time Behavior of Energy in Some Slowly Decreasing Solutions of the Navier-Stokes Equations.- A Selected Survey of the Mathematical Theory of 1D Flows.- A Numerical Method for Nonstationary Stokes Flow.- A New Criterion for Partial Regularity of Suitable Weak Solutions to the Navier-Stokes Equations.- An In Vitro Device for Evaluation of Cellular Response to Flows Found at the Apex of Arterial Bifurcations.