The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.
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1. From particles to fluids (R. Esposito, M. Pulvirenti).
2. Two dimensional Euler system and the vortex patches problem (J.-Y. Chemin).
3. Harmonic analysis tools for solving the incompressible Navier-Stokes equations (M. Cannone).
4. Boundary layers (E. Grenier).
5. Stability of large-amplitude shock waves of compressible Navier-Stokes equations (K. Zumbrun, H. K. Jenssen, G. Lyng).
6. Some mathematical problems in geophysical fluid dynamics (R. Temam, M. Ziane).