**Auteur :** Heinz-Otto Kreiss

**la langue :** en

**Éditeur:** SIAM

**Date de sortie :** 2004-01-01

Initial-Boundary Value Problems and the Navier-Stokes Equations gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs. Applications to parabolic and hyperbolic systems are emphasized in this text. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The book explains the principles of these subjects. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. Audience: when the book was written, the main intent was to write a text on initial-boundary value problems that was accessible to a rather wide audience. Functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplifications have been used throughout. This book continues to be useful to researchers and graduate students in applied mathematics and engineering.

**Auteur :** Heinz-Otto Kreiss

**la langue :** en

**Éditeur:** SIAM

**Date de sortie :** 1989-01-01

Annotation This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.

**Auteur :**

**la langue :** en

**Éditeur:** Academic Press

**Date de sortie :** 1989-06-01

Initial-Boundary Value Problems and the Navier-Stokes Equations

**Auteur :** S.N. Antontsev

**la langue :** en

**Éditeur:** Elsevier

**Date de sortie :** 1989-12-18

The objective of this book is to report the results of investigations made by the authors into certain hydrodynamical models with nonlinear systems of partial differential equations. The investigations involve the results concerning Navier-Stokes equations of viscous heat-conductive gas, incompressible nonhomogeneous fluid and filtration of multi-phase mixture in a porous medium. The correctness of the initial boundary-value problems and the qualitative properties of solutions are also considered. The book is written for those who are interested in the theory of nonlinear partial differential equations and their applications in mechanics.

**Auteur :**

**la langue :** en

**Éditeur:**

**Date de sortie :** 2015

Abstract: In this paper, we study the initial and boundary value problem of the Navier–Stokes equations in the half space. We prove the unique existence of weak solution u ∈ L q ( R + n × ( 0, T ) ) with ∇ u ∈ L l o c q 2 ( R + n × ( 0, T ) ) for a short time interval when the initial data h ∈ B q − 2 q ( R + n ) and the boundary data g ∈ L q ( 0, T ; B q − 1 q ( R n − 1 ) ) + L q ( R n − 1 ; B q − 1 2 q ( 0, T ) ) with normal component g n ∈ L q ( 0, T ; B ̇ q − 1 q ( R n − 1 ) ), n + 2

**Auteur :** Giovanni P. Galdi

**la langue :** en

**Éditeur:** Birkhäuser

**Date de sortie :** 2012-12-06

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.

**Auteur :** Klaus Gürlebeck

**la langue :** en

**Éditeur:** Springer

**Date de sortie :** 2016-01-01

This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail. All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schrödinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topics include spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushkelishvili formulas in linear elasticity. Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis.