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.
1. Chapter 1. Introduction: Fundamental motivations and basic prerequisites for the mathematical analysis of turbulent flows - p. 1 2. Chapter 2. On weak and strong solutions: Analysis of two relevant classes of solutions to the NSE: theorems of existence, uniqueness, and partial (time) regularity - p. 31 3. Chapter 3. Global energy conservation: A review of sufficient conditions ensuring the energy conservation for weak solutions - p. 77 4. Chapter 4. Local energy inequality: From partial regularity to turbulence modeling - p. 131 5. Chapter 5. Numerical construction of physically reasonable solutions: Numerical methods and local energy inequality - p. 187 6. Chapter 6. Long-time behavior of the energy: The Reynolds equations and certain finite-dimensional approximations - p. 255 7. Index - p. 311
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.
1. Chapter 1. Introduction: Fundamental motivations and basic prerequisites for the mathematical analysis of turbulent flows - p. 1 2. Chapter 2. On weak and strong solutions: Analysis of two relevant classes of solutions to the NSE: theorems of existence, uniqueness, and partial (time) regularity - p. 31 3. Chapter 3. Global energy conservation: A review of sufficient conditions ensuring the energy conservation for weak solutions - p. 77 4. Chapter 4. Local energy inequality: From partial regularity to turbulence modeling - p. 131 5. Chapter 5. Numerical construction of physically reasonable solutions: Numerical methods and local energy inequality - p. 187 6. Chapter 6. Long-time behavior of the energy: The Reynolds equations and certain finite-dimensional approximations - p. 255 7. Index - p. 311
