Global Existence and Uniqueness of Nonlinear Evolutionary Fluid Equations
This book presents recent results on nonlinear evolutionary fluid equations such as the compressible (radiative) magnetohydrodynamics (MHD) equations, compressible viscous micropolar fluid equations, the full non-Newtonian fluid equations and non-autonomo
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Yuming Qin Xin Liu Taige Wang
Global Existence and Uniqueness
of Nonlinear
Evolutionary
Fluid Equations
Frontiers in Mathematics
Advisory Editorial Board Leonid Bunimovich (Georgia Institute of Technology, Atlanta) Benoît Perthame (Université Pierre et Marie Curie, Paris) Laurent Saloff-Coste (Cornell University, Ithaca) Igor Shparlinski (Macquarie University, New South Wales) Wolfgang Sprössig (TU Bergakademie Freiberg) Cédric Villani (Institut Henri Poincaré, Paris)
Yuming Qin • Xin Liu • Taige Wang
Global Existence and Uniqueness of Nonlinear Evolutionary Fluid Equations
Yuming Qin Department of Applied Mathematics Donghua University Shanghai, China
Xin Liu Business Information Management School Shanghai Institute of Foreign Trade Shanghai, China
Taige Wang Department of Mathematics Virginia Tech Blacksburg, VA, USA
ISSN 1660-8046 Frontiers in Mathematics ISBN 978-3-0348-0593-3 DOI 10.1007/978-3-0348-0594-0
ISSN 1660-8054 (electronic) ISBN 978-3-0348-0594-0 (eBook)
Library of Congress Control Number: 2015932229 Mathematics Subject Classification (2010): 76-XX, 76A05, 76D05, 76Wxx Springer Basel Heidelberg New York Dordrecht London © Springer Basel 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Basel AG is part of Springer Science+Business Media (www.birkhauser-science.com)
To our Parents
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
1 Global Existence and Asymptotic Behavior of Solutions to the Cauchy Problem of the 1D Compressible Magnetohydrodynamic Fluid System 1.1 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Global Existence and Asymptotic Behavior in H 1 (R) . . . . . . . 1.3 Global Existence and Asymptotic Behavior in H 2 (R) . . . . . . . 1.4 Global Existence and Asymptotic Behavior in H 4 (R) . . . . . . . 1.5 Bibliographic Comments . . . . . . . . . . . . . . . . . . . . . . .
. . . . .
1 4 12 17 27
2 Global Existenc
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