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 < 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 ( - ) 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–Stokes Equations in the L–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’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' 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.

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.