Global Existence of Spherically Symmetric Solutions for Nonlinear Compressible Non-autonomous Navier-Stokes Equations
This chapter concerns the global existence of spherically symmetric solutions for nonlinear compressible non-autonomous Navier-Stokes equations of an initial boundary value problem with an external force and a heat source in bounded annular domains\( {G_n
- PDF / 2,149,148 Bytes
- 181 Pages / 476.22 x 680.32 pts Page_size
- 13 Downloads / 194 Views
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 Lan Huang
Global Well-posedness of Nonlinear Parabolic-Hyperbolic
Coupled Systems
Yuming Qin Department of Applied Mathematics Donghua University Shanghai People’s Republic of China
Lan Huang College of Mathematics and Information Science North China University of Water Sources and Electric Power Zhengzhou People’s Republic of China
ISSN 1660-8046 e-ISSN 1660-8054 ISBN 978-3-0348-0279-6 e-ISBN 978-3-0348-0280-2 DOI 10.1007/978-3-0348-0280-2 Springer Basel Dordrecht Heidelberg London New York Library of Congress Control Number: 2012931854 Mathematics Subject Classification (2010): 35Q30, 76-XX, 76D05 © Springer Basel AG 2012 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use, permission of the copyright owner must be obtained. Printed on acid-free paper
Springer Basel AG is part of Springer Science+Business Media www.birkhauser-science.com
To our parents Zhenrong Qin
Xilan Xia
and Shaolin Huang
Chuanfeng Yang
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
1 Global Existence of Spherically Symmetric Solutions for Compressible Non-autonomous Navier-Stokes Equations 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . 1.2 Global Existence of Solutions in 𝐻 1 . . . . . . . 1.3 Global Existence of Solutions in 𝐻 2 . . . . . . . 1.4 Global Existence of Solutions in 𝐻 4 . . . . . . . 1.5 Bibliographic Comments . . . . . . . . . . . . . .
Nonlinear . . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
1 4 19 25 32
2 Global Existence and Exponential Stability for a Real Viscous Heat-conducting Flow with Shear Viscosity 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Proof of Theorem 2.1.1 . . . . . . . . . . . . . . . . . . . 2.3 Proof of Theorem 2.1.2 . . . . . . . . . . . . . . . . . . . 2.4 Proof of Theorem 2.1.3 . . . . . . . . . . . . . . . . . . . 2.5 Bibliographic Comments . . . . . . . . . . . . . . . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
33 38 46 53 73
3 Regularity and Exponential Stability Fluid in One Space Dimension 3.1 Introduction . . . . . . . . . . 3.2 Proof of Theorem 3.1.1 . . . . 3.3 Proof of Theorem 3.1.2 . . . . 3.4 Bibliographic Comments . . .
75 78 89 91
of the 𝒑th Power Newtonian . . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
Data Loading...