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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.
This volume brings together four contributions to mathematical
fluid mechanics, a classical but still highly active research
field. The contributions cover not only the classical Navier-Stokes
equations and Euler equations, but also some simplified models, and
fluids interacting with elastic walls. The questions addressed in
the lectures range from the basic problems of existence/blow-up of
weak and more regular solutions, to modeling and aspects related to
numerical methods. This book covers recent advances in several
important areas of fluid mechanics. An output of the CIME Summer
School "Progress in mathematical fluid mechanics" held in Cetraro
in 2019, it offers a collection of lecture notes prepared by T.
Buckmaster, (Princeton), S. Canic (UCB) P. Constantin (Princeton)
and A. Kiselev (Duke). These notes will be a valuable asset for
researchers and advanced graduate students in several aspects of
mathematicsl fluid mechanics.
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