Bøger i Advances in Mathematical Fluid Mechanics serien

This volume examines current research in mechanics and its applications to various disciplines, with a particular focus on fluid-structure interaction (FSI). The topics have been chosen in commemoration of Dr. Bong Jae Chung and with respect to his wide range of research interests. This volume stands apart because of this diversity of interests, featuring an interdisciplinary and in-depth analysis of FSI that is difficult to find conveniently collected elsewhere in the literature. Contributors include mathematicians, physicists, mechanical and biomechanical engineers, and psychologists. This volume is structured into four thematic areas in order to increase its accessibility: theory, computations, experiments, and applications. Recent Advances in Mechanics and Fluid-Structure Interaction with Applications will appeal to established researchers as well as postdocs and graduate students interested in this active area of research.

This volume offers an overview of the area of waves in fluids and the role they play in the mathematical analysis and numerical simulation of fluid flows. Based on lectures given at the summer school "e;Waves in Flows"e;, held in Prague from August 27-31, 2018, chapters are written by renowned experts in their respective fields. Featuring an accessible and flexible presentation, readers will be motivated to broaden their perspectives on the interconnectedness of mathematics and physics. A wide range of topics are presented, working from mathematical modelling to environmental, biomedical, and industrial applications. Specific topics covered include:Equatorial wave-current interactionsWater-wave problemsGravity wave propagationFlow-acoustic interactions Waves in Flows will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.

This volume will offer pathways to further research for those interested in the active field of free boundary problems in fluid mechanics, and specifically the two-phase problem for the Navier-Stokes equations.The authors' main focus is on the evolution of an isolated mass with and without surface tension on the free interface.

This volume offers an overview of the area of waves in fluids and the role they play in the mathematical analysis and numerical simulation of fluid flows. A wide range of topics are presented, working from mathematical modelling to environmental, biomedical, and industrial applications.

This volume explores a range of recent advances in mathematical fluid mechanics, covering theoretical topics and numerical methods.

Many problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations. This book is an introduction to the problems involving singular limits based on the concept of weak or variational solutions.

This book provides a comprehensive and consolidated reference for the multipolar fluid model. It presents applications of the model to standard as well as non-standard problems.

This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics.

This monograph considers the motion of incompressible fluids described by the Navier-Stokes equations with large inflow and outflow, and proves the existence of global regular solutions without any restrictions on the magnitude of the initial velocity, the external force, or the flux.

This monograph focuses on the partial regularity theorem, as developed by Caffarelli, Kohn, and Nirenberg (CKN), and offers a proof of the upper bound on the Hausdorff dimension of the singular set of weak solutions of the Navier-Stokes inequality, while also providing a clear and insightful presentation of Scheffer's constructions showing their bound cannot be improved. A short, complete, and self-contained proof of CKN is presented in the second chapter, allowing the remainder of the book to be fully dedicated to a topic of central importance: the sharpness result of Scheffer. Chapters three and four contain a highly readable proof of this result, featuring new improvements as well. Researchers in mathematical fluid mechanics, as well as those working in partial differential equations more generally, will find this monograph invaluable.

This book aims to face particles in flows from many different, but essentially interconnected sides and points of view. Thus the selection of authors and topics represented in the chapters, ranges from 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.

This book summarizes the main advances in the field of nonlinear evolution and pattern formation caused by longwave instabilities in fluids. It will allow readers to master the multiscale asymptotic methods and become familiar with applications of these methods in a variety of physical problems. Longwave instabilities are inherent to a variety of systems in fluid dynamics, geophysics, electrodynamics, biophysics, and many others. The techniques of the derivation of longwave amplitude equations, as well as the analysis of numerous nonlinear equations, are discussed throughout. This book will be of value to researchers and graduate students in applied mathematics, physics, and engineering, in particular within the fields of fluid mechanics, heat and mass transfer theory, and nonlinear dynamics.

This book offers a thorough guide starting from fundamental functional analysis leading to the coupling of Stokes and Darcy equations, including numerical analysis and scientific computing.

There are several physico-chemical processes that determine the behavior of multiphase fluid systems - e.g., the fluid dynamics in the different phases and the dynamics of the interface(s), mass transport between the fluids, adsorption effects at the interface, and transport of surfactants on the interface - and result in heterogeneous interface properties. In general, these processes are strongly coupled and local properties of the interface play a crucial role. A thorough understanding of the behavior of such complex flow problems must be based on physically sound mathematical models, which especially account for the local processes at the interface.This book presents recent findings on the rigorous derivation and mathematical analysis of such models and on the development of numerical methods for direct numerical simulations. Validation results are based on specifically designed experiments using high-resolution experimental techniques. A special feature of this book is its focus on an interdisciplinary research approach combining Applied Analysis, Numerical Mathematics, Interface Physics and Chemistry, as well as relevant research areas in the Engineering Sciences. The contributions originated from the joint interdisciplinary research projects in the DFG Priority Programme SPP 1506 "Transport Processes at Fluidic Interfaces."

This book summarizes the main advances in the field of nonlinear evolution and pattern formation caused by longwave instabilities in fluids. It will allow readers to master the multiscale asymptotic methods and become familiar with applications of these methods in a variety of physical problems. Longwave instabilities are inherent to a variety of systems in fluid dynamics, geophysics, electrodynamics, biophysics, and many others. The techniques of the derivation of longwave amplitude equations, as well as the analysis of numerous nonlinear equations, are discussed throughout. This book will be of value to researchers and graduate students in applied mathematics, physics, and engineering, in particular within the fields of fluid mechanics, heat and mass transfer theory, and nonlinear dynamics.

There are several physico-chemical processes that determine the behavior of multiphase fluid systems ¿ e.g., the fluid dynamics in the different phases and the dynamics of the interface(s), mass transport between the fluids, adsorption effects at the interface, and transport of surfactants on the interface ¿ and result in heterogeneous interface properties. In general, these processes are strongly coupled and local properties of the interface play a crucial role. A thorough understanding of the behavior of such complex flow problems must be based on physically sound mathematical models, which especially account for the local processes at the interface.This book presents recent findings on the rigorous derivation and mathematical analysis of such models and on the development of numerical methods for direct numerical simulations. Validation results are based on specifically designed experiments using high-resolution experimental techniques. A special feature of this book is its focus on an interdisciplinary research approach combining Applied Analysis, Numerical Mathematics, Interface Physics and Chemistry, as well as relevant research areas in the Engineering Sciences. The contributions originated from the joint interdisciplinary research projects in the DFG Priority Programme SPP 1506 ¿Transport Processes at Fluidic Interfaces.¿

This book aims to face particles in flows from many different, but essentially interconnected sides and points of view. Thus the selection of authors and topics represented in the chapters, ranges from 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.

Offering a unique contribution - by exploring in detail the "synergy" of analytical and numerical methods - the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics.

The aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equations and other related equations.

Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics.

This book presents, in a methodical way, updated and comprehensive descriptions and analyses of some of the most relevant problems in the context of fluid-structure interaction (FSI).

This volume consists of six articles, each treating an important topic in the theory ofthe Navier-Stokes equations, at the research level. At that time it was decided that this volume should be published in association with the journal, and expanded to include articles by J.

Lions introduced a "perturbation" of the Navier Stokes equations in which he added in the linear momentum equation the hyper dissipative term (-Ll),Bu, f3 ~ 5/4, where Ll is the Laplace operator.

This volume consists of six articles, each treating an important topic in the theory ofthe Navier-Stokes equations, at the research level. At that time it was decided that this volume should be published in association with the journal, and expanded to include articles by J.

This volume collects the contributions of a Conference held in June 2005 at the laboratoire Paul Painleve (UMR CNRS 8524) in Lille, France. The meeting was intended to review hot topics and future trends in fluid dynamics, with the objective to foster exchanges of various viewpoints (e.g.

This monograph presents recent and new ideas arising from the study of problems of planar fluid dynamics, and which are interesting from the point of view of geometric function theory and potential theory. Additionally, Hele-Shaw flows on parameter spaces are discussed, and connections with string theory are revealed.

Lions introduced a "perturbation" of the Navier Stokes equations in which he added in the linear momentum equation the hyper dissipative term (-Ll),Bu, f3 ~ 5/4, where Ll is the Laplace operator.