Preface; Contents; 1 A Maximal Regularity Approach to the Analysis of Some Particulate Flows; 1.1 Introduction and Hilbert Space Analysis of a Toy Model; 1.1.1 The General Context; 1.1.2 Introduction of a Toy Model; 1.1.3 Change of Variables; 1.1.4 Local in Time Existence and Uniqueness of Solutions; 1.1.5 Proof of the Global Well-Posedness Result; 1.1.6 Bibliographical Notes; 1.2 Examples of Systems Modelling Fluid-Structure Interactions; 1.2.1 Motion of a Piston in a Heat Conducting Gas; a 1DModel; 1.2.2 Motion of a Rigid Body in a Viscous IncompressibleFluid. 1.2.3 Motion of a Solid in a Compressible Fluid1.3 Short Introduction to R-Sectorial Operators; 1.3.1 Basic Definitions; 1.3.2 Weis' Theorem; 1.3.3 Abstract Framework Corresponding to Linear Fluid-Solid Interaction Problems; 1.3.4 Bibliographical Notes; 1.4 Existence and Uniqueness Results; 1.4.1 Some Background; 1.4.2 Back to the Toy Problem; 1.4.3 A More Realistic 1D Model; 1.4.4 Motion of a Solid in a Compressible Fluid; 1.4.5 Bibliographical Notes; References; 2 Time-Periodic Linearized Navier-Stokes Equations: An Approach Based on Fourier Multipliers; 2.1 Introduction; 2.2 Preliminaries. General Vector SpacesSpaces of Continuous Functions; Lebesgue Spaces; Locally Compact Abelian Groups; Haar Measure; Convolution; Fourier Transform; Finite Products; Closed Subgroups and Quotient Groups; 2.3 Transference Principle for Multipliers; 2.3.1 Basic Properties of Fourier Multipliers; 2.3.2 Approximation Results; 2.3.3 Another Characterization of Multipliers; 2.3.4 The Transference Principle; 2.4 The Schwartz-Bruhat Space; 2.4.1 Elementary Groups; 2.4.2 Good and Compactly Generated Open Subgroups; 2.4.3 The General Schwartz-Bruhat Space; 2.4.4 Embedding Results.

This book aims to face particles inflows from many different, but essentially interconnected sides and points of view. Thus the selection of authors and topics represented in the chapters, ranges from the deep mathematical analysis of the associated models, through the techniques of their numerical solution, towards real applications and physical implications. The scope and structure of the book as well as the selection of authors was motivated by the very successful summer course and workshop "Particles in Flows'' that was held in Prague in the August of 2014. This meeting revealed the need for a book dealing with this specific and challenging multidisciplinary subject, i.e. particles in industrial, environmental and biomedical flows and the combination of fluid mechanics, solid body mechanics with various aspects of specific applications.