**Author**: Pierre Gilles Lemarie-Rieusset

**Publisher:** CRC Press

**ISBN:**

**Category:** Mathematics

**Page:** 718

**View:** 779

Up-to-Date Coverage of the Navier–Stokes Equation from an Expert in Harmonic Analysis The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier–Stokes Problem in the 21st Century provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics. The book focuses on incompressible deterministic Navier–Stokes equations in the case of a fluid filling the whole space. It explores the meaning of the equations, open problems, and recent progress. It includes classical results on local existence and studies criterion for regularity or uniqueness of solutions. The book also incorporates historical references to the (pre)history of the equations as well as recent references that highlight active mathematical research in the field.

*Proceedings of the ICASE/LaRC/NSF/ARO Workshop, conducted by the Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, The National Science Foundation and the Army Research Office, April 22–24, 1998*

**Author**: Manuel D. Salas

**Publisher:** Springer Science & Business Media

**ISBN:**

**Category:** Mathematics

**Page:** 292

**View:** 604

This book is a graduate text on the incompressible Navier-Stokes system, which is of fundamental importance in mathematical fluid mechanics as well as in engineering applications. The goal is to give a rapid exposition on the existence, uniqueness, and regularity of its solutions, with a focus on the regularity problem. To fit into a one-year course for students who have already mastered the basics of PDE theory, many auxiliary results have been described with references but without proofs, and several topics were omitted. Most chapters end with a selection of problems for the reader. After an introduction and a careful study of weak, strong, and mild solutions, the reader is introduced to partial regularity. The coverage of boundary value problems, self-similar solutions, the uniform L3 class including the celebrated Escauriaza-Seregin-Šverák Theorem, and axisymmetric flows in later chapters are unique features of this book that are less explored in other texts. The book can serve as a textbook for a course, as a self-study source for people who already know some PDE theory and wish to learn more about Navier-Stokes equations, or as a reference for some of the important recent developments in the area.

This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of "invisible obstacles." In Chapter 5, it provides a solution to the Navier‒Stokes problem in R3. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier‒Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies.

Towards the close of the 20th century, the world's leading experts in theoretical and experimental physics review the major developments in their respective research areas, and present the prospects for the coming 21st century. The subjects covered in this volume are field theory, string theory, quantum cosmology, solid state physics, physics of complex systems, high energy physics, quark–gluon plasma, nuclear physics and observational cosmology. Contents:Three Stages, Three Modes, and Beyond (Y Nambu)Quantum Transport in Mesoscopic Semiconductor Structures (T Ando)Nonequilibrium Physics and the Origins of Complexity in Nature (J S Langer)New Horizon in Nuclear Physics and Astrophysics Using Radioactive Nuclear Beams (I Tanihata)The Future of Particle Physics (F Wilczek & D J Gross)Status and Prospects of Relativistic Heavy-Ion Experiments (S Nagamiya)Present and Future of High Energy Physics with Hadron Colliders (K Kondo)Cosmological Parameters and Evolution of Galaxies: An Observational Perspective (S Okamura)Quantum Cosmology: Problems for the 21st Century (J B Hartle) Readership: Physicists. keywords:Theoretical Physics;Experimental Physics;Field Theory;String Theory;Quantum Cosmology;Solid State Physics;Quark-Gluon Plasma;High Energy Physics;Nuclear Physics;Cosmology

This volume provides a snapshot of the current and future trends in turbulence research across a range of disciplines. It provides an overview of the key challenges that face scientific and engineering communities in the context of huge databases of turbulence information currently being generated, yet poorly mined. These challenges include coherent structures and their control, wall turbulence and control, multi-scale turbulence, the impact of turbulence on energy generation and turbulence data manipulation strategies. The motivation for this volume is to assist the reader to make physical sense of these data deluges so as to inform both the research community as well as to advance practical outcomes from what is learned. Outcomes presented in this collection provide industry with information that impacts their activities, such as minimizing impact of wind farms, opportunities for understanding large scale wind events and large eddy simulation of the hydrodynamics of bays and lakes thereby increasing energy efficiencies, and minimizing emissions and noise from jet engines. Elucidates established, contemporary, and novel aspects of fluid turbulence - a ubiquitous yet poorly understood phenomena; Explores computer simulation of turbulence in the context of the emerging, unprecedented profusion of experimental data,which will need to be stewarded and archived; Examines a compendium of problems and issues that investigators can use to help formulate new promising research ideas; Makes the case for why funding agencies and scientists around the world need to lead a global effort to establish and steward large stores of turbulence data, rather than leaving them to individual researchers.

Computational science can loosely be defined as the endeavor to develop and analyse models for the simulation and control of complex processes. This is achieved by making optimal use of computer resources and by drawing upon a variety of disciplines, techniques and theories. With the emergence of advanced computational and information technologies, computational science now has a significant impact on engineering, physical, biological, management and social sciences. The contributions in this state-of-the-art volume range from theoretical and numerical topics to practical implementations. The subject matter includes modelling, mathematical and numerical analysis, differential equations, linear algebra, optimization, domain decomposition, computational fluid dynamics, computational mechanics, elasticity, structure, computational physics and chemistry, electromagnetic, control theory and other applications. This volume is dedicated to Roland Glowinski on the occasion of his 60th birthday. It is aimed at the next generation of scientists, applied mathematicians, computer scientists, practitioners and engineers who will define computational science within the context of the challenging scientific, industrial, economic and societal problems of the 21st century.

The International Mining Forum is a meeting of scientists and professionals for exchanging new ideas and experiences, evaluate previously implemented solutions, and discuss fresh ideas that might change the mining industry’s image. In recent years theory and technology in mine safety and efficient exploitation has made considerable progress in China, Poland and other countries, due to the introduction of many new theories and technologies. The International Mining Forum 2010, jointly organized by Anhui University of Science and Technology (China), AGH University of Science and Technology (Poland) and Mineral and Energy Economy Research Institute of the Polish Academy of Sciences (Poland), has provided experts all over the world with an opportunity and platform to exchange information and ideas. Purpose of the forum was to promote research and development of mine safety, efficient exploitation theory and provide theoretical and technical support for mine safety improvement. This book is addressed to researchers and professionals who work in the fields of underground mining technology, rock engineering or mine management.

This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory" provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.

Presenting a fun and educational way to explore the wonders of the world of science, this newly updated edition poses and answers 2,200 questions, providing an abundance of original and interesting science facts. Children and adults will uncover some of the most interesting, unusual, and quirky science curiosities such as: Are cell phones dangerous to your health? Is the same strain of yeast used to make different types of beer? What is the cleanest fossil fuel? What is the largest invertebrate? Readers will find this informative and enjoyable resource is chock full of hundreds of intriguing science and technology topics, from the inner workings of the human body and outer space to math, computers, planes, trains, and automobiles.