Local Well-Posedness and Break-Down Criterion of the Incompressible Euler Equations with Free Boundary, Zarate Ceballos, Henry Parra Amaris, Jorge Ernesto Jimenez Jimenez, Hernan Romero Rincon, Diego Alexis Agudelo Rojas, Oscar Ortiz Trivino, Jorge Eduardo
Описание: Telling the stories of twelve North Carolina heritage foods, each matched to the month of its peak readiness for eating, Georgann Eubanks takes readers on a flavourful journey across the state. Talking with farmers, fishmongers, cooks, historians, and scientists, Eubanks looks at how foods are deeply tied to the culture of the Old North State.
Описание: This monograph presents an original, concise mathematical theory for bio-mimetic swimmers in the framework of a coupled system of PDEs and ODEs.
Описание: The aim of this book is to provide beginning graduate students who completed the first two semesters of graduate-level analysis and PDE courses with a first exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces.Chapters 1 and 2 cover the fundamentals of the Euler theory: derivation, Eulerian and Lagrangian perspectives, vorticity, special solutions, existence theory for smooth solutions, and blowup criteria. Chapters 3, 4, and 5 cover the fundamentals of the Navier-Stokes theory: derivation, special solutions, existence theory for strong solutions, Leray theory of weak solutions, weak-strong uniqueness, existence theory of mild solutions, and Prodi-Serrin regularity criteria. Chapter 6 provides a short guide to the must-read topics, including active research directions, for an advanced graduate student working in incompressible fluids. It may be used as a roadmap for a topics course in a subsequent semester. The appendix recalls basic results from real, harmonic, and functional analysis. Each chapter concludes with exercises, making the text suitable for a one-semester graduate course.Prerequisites to this book are the first two semesters of graduate-level analysis and PDE courses.
Описание: Provides graduate students with exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces.
Описание: This monograph explores the motion of incompressible fluids by presenting and incorporating various boundary conditions possible for real phenomena.
Описание: The numerical treatment of the evolutionary incompressible Navier-Stokes equations, which determine many practicaIly relevant fluid flows, is an area of considerable interest for industrial as weIl as scientific applications. Im- portant for drawing furt her conclusions for the behavior of certain flows in diverse disciplines such as (astro-)physics, engineering, meteorology, oceanog- raphy, or biology is a reliable, robust and efficient numerical model. The goal of computing highly complex flows requires the development of sophisticated algorithms. In general, numerical schemes which do not cause high computa- tional cost, often suffer from stability or reliability problems and vice versa. So, it demands a numerical and physical a-priori knowledge from the user in order to select the "best fitting algorithm" for a particular problem under consideration. The use of knowledge about physical phenomena appearing in a specific problem aIlows the relaxation of some robustness-conditions that otherwise need to be imposed on the numerical scheme in order to ensure reliability with respect to the convergence behavior. To this end, this leads to permittance of numerical models simulating continuous flows which do not satisfy severe stability restrictions that lead to robust schemes, with the advantage of lower computational costs necessary to obtain the same accu- racy. A major part of this book is devoted to such schemes that are of great importance: classical projection methods 01 high er order and nonstationary quasi-compressibility methods.
Описание: This book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures.
Описание: Presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures. This book discusses the conditions required to satisfy the no-slip boundary conditions in the various formulations. For each formulation, it provides a statement of the mathematical problem.
Автор: Guilong Gui Название: Stability to the Incompressible Navier-Stokes Equations ISBN: 3642430678 ISBN-13(EAN): 9783642430671 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This thesis contains results of Dr. Guilong Gui during his PhD period with the aim to understand incompressible Navier-Stokes equations. It is devoted to the study of the stability to the incompressible Navier-Stokes equations. There is great potential for further theoretical and numerical research in this field. The techniques developed in carrying out this work are expected to be useful for other physical model equations. It is also hopeful that the thesis could serve as a valuable reference on current developments in research topics related to the incompressible Navier-Stokes equations. It was nominated by the Graduate University of Chinese Academy of Sciences as an outstanding PhD thesis.
Описание: This thesis presents an accurate and advanced numerical methodology to remedy difficulties such as direct numerical simulation of magnetohydrodynamic (MHD) flow in computational fluid dynamics (CFD), grid generation processes in tokamak fusion facilities, and the coupling between the surface tension force and Lorentz force in the metallurgical industry. In addition, on the basis of the numerical platform it establishes, it also investigates selected interesting topics, e.g. single bubble motion under the influence of either vertical or horizontal magnetic fields. Furthermore, it confirms the relation between the bubble’s path instability and wake instability, and observes the anisotropic (isotropic) effect of the vertical (horizontal) magnetic field on the vortex structures, which determines the dynamic behavior of the rising bubble. The direct numerical simulation of magnetohydrodynamic (MHD) flows has proven difficult in the field of computational fluid dynamic (CFD) research, because it not only concerns the coupling of the equations governing the electromagnetic field and the fluid motion, but also calls for suitable numerical methods for computing the electromagnetic field. In tokamak fusion facilities, where the MHD effect is significant and the flow domain is complex, the process of grid generation requires considerable time and effort. Moreover, in the metallurgical industry, where multiphase MHD flows are usually encountered, the coupling between the surface tension force and Lorentz force adds to the difficulty of deriving direct numerical simulations.
Автор: Michael Reissig; Michael Ruzhansky Название: Progress in Partial Differential Equations ISBN: 3319001248 ISBN-13(EAN): 9783319001241 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations.
Автор: A. Iacob; A. Ashyralyev; P.E. Sobolevskii Название: Well-Posedness of Parabolic Difference Equations ISBN: 3034896611 ISBN-13(EAN): 9783034896610 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy.
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