Three-Dimensional Navier-Stokes Equations for Turbulence provides a rigorous but still accessible account of research into local and global energy dissipation, with particular emphasis on turbulence modeling. The mathematical detail is combined with coverage of physical terms such as energy balance and turbulence to make sure the reader is always in touch with the physical context. All important recent advancements in the analysis of the equations, such as rigorous bounds on structure functions and energy transfer rates in weak solutions, are addressed, and connections are made to numerical methods with many practical applications.
The book is written to make this subject accessible to a range of readers, carefully tackling interdisciplinary topics where the combination of theory, numerics, and modeling can be a challenge.
- Includes a comprehensive survey of modern reduced-order models, including ones for data assimilation
- Includes a self-contained coverage of mathematical analysis of fluid flows, which will act as an ideal introduction to the book for readers without mathematical backgrounds
- Presents methods and techniques in a practical way so they can be rapidly applied to the reader’s own work
1. Introduction
2. On weak and strong solutions
3. Global energy conservation
4. Local energy inequality
5. Numerical construction of physically reasonable solutions
6. Long-time behavior of the energy
Luigi C. Berselli has been a full professor of Mathematical Analysis since 2015, and previously held positions of adjunct and associate professor, all at the Università di Pisa, Italy. He also has held visiting professorships at several institutions, including la Scuola Normale Superiore di Pisa, SISSA Trieste, the University of Rennes, and the University of Freiburg. Throughout his research career he has been very interested in both theoretical and applied analysis of PDEs, especially the initial-boundary value problems related to incompressible Newtonian and non-Newtonian fluids, with applications to turbulence, biomedical engineering, and geophysical flows. He is author of about 80 research papers in international journals and 1 monograph published in 2006. He has recently organized several conferences and is associate editor for 3 journals.
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