Mathematical Topics in Fluid Mechanics: Volume 2: Compressible Models
Series: Oxford Lecture Series in Mathematics and Its Applications; 10;
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Product details:
- Edition number and title :Volume 2: Compressible Models
- Publisher OUP Oxford
- Date of Publication 19 March 1998
- ISBN 9780198514886
- Binding Hardback
- No. of pages364 pages
- Size 242x162x23 mm
- Weight 681 g
- Language English 0
Categories
Short description:
Fluid mechanics models consist of systems of nonlinear partial differential equations for which, despite a long history of important mathematical contributions, no complete mathematical understanding is available. The second volume of this book describes compressible fluid-mechanics models. The book contains entirely new material on a subject known to be rather difficult and important for applications (compressible flows). It is probably a unique effort on the mathematical problems associated with the compressible Navier-Stokes equations, written by one of the world's leading experts on nonlinear partial differential equations. Professor P.L. Lions won the Fields Medal in 1994.
MoreLong description:
This series of books forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models. These models consist of systems of nonlinear partial differential equations such as the incompressible and compressible NavierStokes equations. The main emphasis in the first volume is on the mathematical analysis of incompressible models. The second volume is an attempt to achieve a mathematical understanding of compressible Navier-Stokes equations. It is probably the first reference covering the issue of global solutions in the large. It includes entirely new material on compactness properties of solutions for the Cauchy problem, the existence and regularity of stationary solutions, and the existence of global weak solutions. Written by one of the world's leading researchers in nonlinear partial differential equations, Mathematical Topics in Fluid Mechanics will be an indispensable reference for every serious researcher in the field. Its topicality and the clear, concise, and deep presentation by the author make it an outstanding contribution to the great theoretical problems in science concerning rigorous mathematical modelling of physical phenomena. Pierre-Louis Lions is Professor of Mathematics at the University Paris-Dauphine and of Applied Mathematics at the Ecole Polytechnique.
MoreTable of Contents:
Part II: Compressible models
Compactness results for compressible isentropic Navier-Stokes equations
Stationary problems
Existence results for Cauchy problems
Related problems
Appendix A. A few facts about some function spaces
Appendix B. On a weakly continuous product
Appendix C. A remark on the limiting case for Sobolev inequalities
Appendix D. Continua and limits
Appendix E. On sums of Lp spaces
Appendix F. A remark on parabolic equations
Bibliography of Volumes 1 and 2
Erratum (Volume 1)
Index
