Couverture / Jaquette

One of the most challenging topics in applied mathematics has been the development of the theory of nonlinear partial differential equations. Despite a long history of contributions, there exists no central core theory. This two volume work forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models.

Note biographique

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.

Table des matières

• Preface


• Table of contents


• 1: Presentation of the models


• Part 1: Incompressible Models


• 2: Density-dependent Navier-Stokes equations


• 3: Navier-Stokes equations


• 4: Euler equations and other incompressible models


• Appendix A Truncation of divergence-free vectorfields


• Appendix B Two facts on D1,2(R2)


• Appendix C Compactness in time with values in weak topologies


• Appendix D Weak L1 estimates for solutions of the heat equation


• Appendix E A short proof of the existence of renormalized solutions for parabolic equations


• Intended Table of Contents of Volume 2


• Part 2: Compressible Models


• 5: Compactness results for compressible isentropic Navier-Stokes


• 6: Stationary problems


• 7: Existence results


• 8: Related questions


• Part 3: Asymptotic limites


• 9: Asymptotic limits

Détails