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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 "Waves in Flows", 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 interactions
Water-wave problems Gravity wave propagation Flow-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 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 "Waves in Flows", 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 interactions
Water-wave problems Gravity wave propagation Flow-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 contributed volume is based on talks given at the August 2016
summer school "Fluids Under Pressure," held in Prague as part of
the "Prague-Sum" series. Written by experts in their respective
fields, chapters explore the complex role that pressure plays in
physics, mathematical modeling, and fluid flow analysis. Specific
topics covered include: Oceanic and atmospheric dynamics
Incompressible flows Viscous compressible flows Well-posedness of
the Navier-Stokes equations Weak solutions to the Navier-Stokes
equations Fluids Under Pressure will be a valuable resource for
graduate students and researchers studying fluid flow dynamics.
This contributed volume is based on talks given at the August 2016
summer school "Fluids Under Pressure," held in Prague as part of
the "Prague-Sum" series. Written by experts in their respective
fields, chapters explore the complex role that pressure plays in
physics, mathematical modeling, and fluid flow analysis. Specific
topics covered include: Oceanic and atmospheric dynamics
Incompressible flows Viscous compressible flows Well-posedness of
the Navier-Stokes equations Weak solutions to the Navier-Stokes
equations Fluids Under Pressure will be a valuable resource for
graduate students and researchers studying fluid flow dynamics.
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 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 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). Generally
speaking, FSI is among the most popular and intriguing problems in
applied sciences and includes industrial as well as biological
applications. Various fundamental aspects of FSI are addressed from
different perspectives, with a focus on biomedical applications.
More specifically, the book presents a mathematical analysis of
basic questions like the well-posedness of the relevant initial and
boundary value problems, as well as the modeling and the numerical
simulation of a number of fundamental phenomena related to human
biology. These latter research topics include blood flow in
arteries and veins, blood coagulation and speech modeling. We
believe that the variety of the topics discussed, along with the
different approaches used to address and solve the corresponding
problems, will help readers to develop a more holistic view of the
latest findings on the subject, and of the relevant open questions.
For the same reason we expect the book to become a trusted
companion for researchers from diverse disciplines, such as
mathematics, physics, mathematical biology, bioengineering and
medicine."
This volume brings together five contributions to mathematical
fluid mechanics, a classical but still very active research field
which overlaps with physics and engineering. The contributions
cover not only the classical Navier-Stokes equations for an
incompressible Newtonian fluid, but also generalized Newtonian
fluids, fluids interacting with particles and with solids, and
stochastic models. The questions addressed in the lectures range
from the basic problems of existence of weak and more regular
solutions, the local regularity theory and analysis of potential
singularities, qualitative and quantitative results about the
behavior in special cases, asymptotic behavior, statistical
properties and ergodicity.
This volume consists of five research articles, each dedicated to a
significant topic in the mathematical theory of the Navier-Stokes
equations, for compressible and incompressible fluids, and to
related questions. All results given here are new and represent a
noticeable contribution to the subject. One of the most famous
predictions of the Kolmogorov theory of turbulence is the so-called
Kolmogorov-obukhov five-thirds law. As is known, this law is
heuristic and, to date, there is no rigorous justification. The
article of A. Biryuk deals with the Cauchy problem for a
multi-dimensional Burgers equation with periodic boundary
conditions. Estimates in suitable norms for the corresponding
solutions are derived for "large" Reynolds numbers, and their
relation with the Kolmogorov-Obukhov law are discussed. Similar
estimates are also obtained for the Navier-Stokes equation. In the
late sixties J. L. 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 term is referred to as an "artificial"
viscosity. Even though it is not physically moti vated, artificial
viscosity has proved a useful device in numerical simulations of
the Navier-Stokes equations at high Reynolds numbers. The paper of
of D. Chae and J. Lee investigates the global well-posedness of a
modification of the Navier Stokes equation similar to that
introduced by Lions, but where now the original dissipative term
-Llu is replaced by (-Ll)O:u, 0 S Ct < 5/4.
This volume consists of six articles, each treating an important
topic in the theory ofthe Navier-Stokes equations, at the research
level. Some of the articles are mainly expository, putting
together, in a unified setting, the results of recent research
papers and conference lectures. Several other articles are devoted
mainly to new results, but present them within a wider context and
with a fuller exposition than is usual for journals. The plan to
publish these articles as a book began with the lecture notes for
the short courses of G.P. Galdi and R. Rannacher, given at the
beginning of the International Workshop on Theoretical and
Numerical Fluid Dynamics, held in Vancouver, Canada, July 27 to
August 2, 1996. A renewed energy for this project came with the
founding of the Journal of Mathematical Fluid Mechanics, by G.P.
Galdi, J. Heywood, and R. Rannacher, in 1998. At that time it was
decided that this volume should be published in association with
the journal, and expanded to include articles by J. Heywood and W.
Nagata, J. Heywood and M. Padula, and P. Gervasio, A. Quarteroni
and F. Saleri. The original lecture notes were also revised and
updated.
On November 3, 2005, Alexander Vasil'evich Kazhikhov left this
world, untimely and unexpectedly. He was one of the most in?uential
mathematicians in the mechanics of ?uids, and will be remembered
for his outstanding results that had, and still have, a c-
siderablysigni?cantin?uenceinthe?eld.Amonghis
manyachievements,werecall that he was the founder of the modern
mathematical theory of the Navier-Stokes equations describing one-
and two-dimensional motions of a viscous, compressible and
heat-conducting gas. A brief account of Professor Kazhikhov's
contributions to science is provided in the following article
"Scienti?c portrait of Alexander Vasil'evich Kazhikhov". This
volume is meant to be an expression of high regard to his memory,
from most of his friends and his colleagues. In particular, it
collects a selection of papers that represent the latest progress
in a number of new important directions of Mathematical Physics,
mainly of Mathematical Fluid Mechanics. These papers are written by
world renowned specialists. Most of them were friends, students or
colleagues of Professor Kazhikhov, who either worked with him
directly, or met him many times in o?cial scienti?c meetings, where
they had the opportunity of discussing problems of common interest.
This book surveys research results on the physical and
mathematical modeling, as well as the numerical simulation of
complex fluid and structural mechanical processes occurring in the
human blood circulation system. Topics treated include continuum
mechanical description; choice of suitable liquid and wall models;
mathematical analysis of coupled models; numerical methods for flow
simulation; parameter identification and model calibration;
fluid-solid interaction; mathematical analysis of piping systems;
particle transport in channels and pipes; artificial boundary
conditions, and many more. The book was developed from lectures
presented by the authors at the Oberwolfach Research Institute
(MFO), in Oberwolfach-Walke, Germany, November, 2005.
This volume consists of five research articles, each dedicated to a
significant topic in the mathematical theory of the Navier-Stokes
equations, for compressible and incompressible fluids, and to
related questions. All results given here are new and represent a
noticeable contribution to the subject. One of the most famous
predictions of the Kolmogorov theory of turbulence is the so-called
Kolmogorov-obukhov five-thirds law. As is known, this law is
heuristic and, to date, there is no rigorous justification. The
article of A. Biryuk deals with the Cauchy problem for a
multi-dimensional Burgers equation with periodic boundary
conditions. Estimates in suitable norms for the corresponding
solutions are derived for "large" Reynolds numbers, and their
relation with the Kolmogorov-Obukhov law are discussed. Similar
estimates are also obtained for the Navier-Stokes equation. In the
late sixties J. L. 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 term is referred to as an "artificial"
viscosity. Even though it is not physically moti vated, artificial
viscosity has proved a useful device in numerical simulations of
the Navier-Stokes equations at high Reynolds numbers. The paper of
of D. Chae and J. Lee investigates the global well-posedness of a
modification of the Navier Stokes equation similar to that
introduced by Lions, but where now the original dissipative term
-Llu is replaced by (-Ll)O:u, 0 S Ct < 5/4.
This set of six papers, written by eminent experts in the field, is
concerned with that part of fluid mechanics that seeks its
foundation in the rigorous mathematical treatment of the
Navier-Stokes equations. In particular, an overview is given on
state of research regarding the global existence of smooth
solutions, for which uniqueness and continuous dependence on the
data can be proven. Then, the book moves on to a discussion of
recent developments of the finite element Galerkin method, with an
emphasis on a priori and a posteriori error estimation and adaptive
mesh refinement. A further article elaborates on spectral Galerkin
methods and their extension to domains with complicated geometries
by employing the techniques of domain decomposition. The rigorous
explanation of bifurcation phenomena in fluids has long been a
central topic in the theory of Navier-Stokes equations. Here,
bifurcation theory is introduced in a general setting that is
particularly convenient for application to such problems. Finally,
the extension of Navier-Stokes theory to compressible viscous
flows, studied in two more papers, opens up a fascinating panorama
of theoretical and numerical problems. While some of the
contributions are expository, others primarily present new results
within a wider context and fuller exposition than is usual for
research papers. The book is meant to introduce researchers and
advanced students to the research level on some of the most
important topics of the field.
This volume presents state-of-the-art developments in theoretical
and applied fluid mechanics. Chapters are based on lectures given
at a workshop in the summer school Fluids under Control, held in
Prague on August 25, 2021. Readers will find a thorough analysis of
current research topics, presented by leading experts in their
respective fields. Specific topics covered include:
Magnetohydrodynamic systems The steady Navier-Stokes-Fourier system
Boussinesq equations Fluid-structure-acoustic interactions Fluids
under Control will be a valuable resource for students
interested in mathematical fluid mechanics.
This volume explores a range of recent advances in mathematical
fluid mechanics, covering theoretical topics and numerical methods.
Chapters are based on the lectures given at a workshop in the
summer school Waves in Flows, held in Prague from August 27-31,
2018. A broad overview of cutting edge research is presented, with
a focus on mathematical modeling and numerical simulations. Readers
will find a thorough analysis of numerous state-of-the-art
developments presented by leading experts in their respective
fields. Specific topics covered include: Chemorepulsion
Compressible Navier-Stokes systems Newtonian fluids Fluid-structure
interactions Waves in Flows: The 2018 Prague-Sum Workshop Lectures
will appeal to post-doctoral students and scientists whose work
involves fluid mechanics.
This book collects together a unique set of articles dedicated to
several fundamental aspects of the Navier-Stokes equations. As is
well known, understanding the mathematical properties of these
equations, along with their physical interpretation, constitutes
one of the most challenging questions of applied mathematics.
Indeed, the Navier-Stokes equations feature among the Clay
Mathematics Institute's seven Millennium Prize Problems (existence
of global in time, regular solutions corresponding to initial data
of unrestricted magnitude). The text comprises three extensive
contributions covering the following topics: (1) Operator-Valued H
-calculus, R-boundedness, Fourier multipliers and maximal
Lp-regularity theory for a large, abstract class of quasi-linear
evolution problems with applications to Navier-Stokes equations and
other fluid model equations; (2) Classical existence, uniqueness
and regularity theorems of solutions to the Navier-Stokes
initial-value problem, along with space-time partial regularity and
investigation of the smoothness of the Lagrangean flow map; and (3)
A complete mathematical theory of R-boundedness and maximal
regularity with applications to free boundary problems for the
Navier-Stokes equations with and without surface tension. Offering
a general mathematical framework that could be used to study fluid
problems and, more generally, a wide class of abstract evolution
equations, this volume is aimed at graduate students and
researchers who want to become acquainted with fundamental problems
related to the Navier-Stokes equations.
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