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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.

Fluid mechanics -- Mathematics. --- Fluid mechanics. --- Fluid mechanics --- Engineering & Applied Sciences --- Civil & Environmental Engineering --- Civil Engineering --- Applied Mathematics --- Mathematics --- Mathematics. --- Math --- Hydromechanics --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Numerical analysis. --- Continuum physics. --- Biomedical engineering. --- Applications of Mathematics. --- Classical Continuum Physics. --- Computational Mathematics and Numerical Analysis. --- Numerical Analysis. --- Biomedical Engineering. --- Science --- Continuum mechanics --- Computer science --- Classical and Continuum Physics. --- Biomedical Engineering and Bioengineering. --- Clinical engineering --- Medical engineering --- Bioengineering --- Biophysics --- Engineering --- Medicine --- Mathematical analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Classical field theory --- Continuum physics --- Physics --- Engineering analysis

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The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost.At the end of each chapter some exercises are posed in order to assist the interested reader in better understanding the concepts presented. Solutions and accompanying remarks are given in the Appendix.

Differential equations --- Finite element method. --- Numerical solutions.

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The interaction of a fluid with a solid body is a widespread phenomenon in nature, occurring at different scales and different applied disciplines. Interestingly enough, even though the mathematical theory of the motion of bodies in a liquid is one of the oldest and most classical problems in fluid mechanics, mathematicians have, only very recently, become interested in a systematic study of the basic problems related to fluid-structure interaction, from both analytical and numerical viewpoints. ""Fundamental Trends in Fluid-Structure Interaction"" is a unique collection of important papers wr

Fluid-structure interaction. --- Structure-fluid interaction --- Fluid dynamics --- Structural dynamics --- Fluid mechanics --- Mécanique des fluides