Mathematical Topics in Fluid Mechanics

Volume 2: Compressible Models
Erscheinungsjahr 2013
ISBN: 978-0-19-967922-5
Verlag: Oxford University Press

Buch, Englisch, 364 Seiten, Print PDF, Format (B × H): 156 mm x 232 mm, Gewicht: 544 g

This second volume works with the first to form 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 unique 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.

Zielgruppe

Postgraduate mathematicians, applied mathematicians; researchers in mathematics and applied mathematics, also fluid mechanics and engineering.

Autoren/Hrsg.

Lions, Pierre-Louis

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Kontinuumsmechanik

Inhaltsverzeichnis

- Part II: Compressible models

- 5: Compactness results for compressible isentropic Navier-Stokes equations

- 6: Stationary problems

- 7: Existence results for Cauchy problems

- 8: 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

Über Autor(innen)

Pierre-Louis Lions is a Professor of Partial differential equations and their applications at Collège de France in Paris and Professor in the Department of Applied Mathematics, Ecole Polytechnique. His work focuses on the theory of nonlinear partial differential equations and he received the Fields Medal for his work in 1994.