Lecture notes of graduate courses given by the authors at Indiana University (1985-86) and the University of Chicago (1986-87). Paper edition, $14.95. Annotation copyright Book News, Inc. Portland, Or.

Navier-Stokes Equations (Chicago Lectures in Mathematics)

Science & Math

Constantin, Peter

Foias, Ciprian

Mathematics

Univ of Chicago Pr

Both an original contribution and a lucid introduction to mathematical aspects of fluid mechanics, Navier-Stokes Equations provides a compact and self-contained course on these classical, nonlinear, partial differential equations, which are used to describe and analyze fluid dynamics and the flow of gases.

Reference

Almanacs & Yearbooks

University of Chicago Press

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).&nbsp; These notes will be a valuable asset for researchers and advanced graduate students in several aspects of mathematicsl fluid mechanics.

Progress in Mathematical Fluid Dynamics: Cetraro, Italy 2019 (C.I.M.E. Foundation Subseries)

Buckmaster, Tristan

Čanić, Sunčica

Kiselev, Alexander A.

Springer

Constantin presents the Euler equations of ideal incompressible fluids and the blow-up problem for the Navier-Stokes equations of viscous fluids, describing major mathematical questions of turbulence theory. These are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations, explained in Gallavotti's lectures. Kazhikhov introduces the theory of strong approximation of weak limits via the method of averaging, applied to Navier-Stokes equations. Y. Meyer focuses on nonlinear evolution equations and related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, localized in space or in time variable. Ukai discusses the asymptotic analysis theory of fluid equations, the Cauchy-Kovalevskaya technique for the Boltzmann-Grad limit of the Newtonian equation, the multi-scale analysis, giving compressible and incompressible limits of the Boltzmann equation, and the analysis of their initial layers.

Mathematical Foundation of Turbulent Viscous Flows: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 1-5, 2003 (Lecture Notes in Mathematics, 1871)

Meyer, Yves

Gallavotti, Giovanni

Kazhikhov, Alexandre V.

Ukai, Seiji

This volume brings together five contributions to mathematical fluid mechanics, a classical but still very active research field which overlaps with physics and engineering. The contributions cover not only the classical Navier-Stokes equations for an incompressible Newtonian fluid, but also generalized Newtonian fluids, fluids interacting with particles and with solids, and stochastic models. The questions addressed in the lectures range from the basic problems of existence of weak and more regular solutions, the local regularity theory and analysis of potential singularities, qualitative and quantitative results about the behavior in special cases, asymptotic behavior, statistical properties and ergodicity.

Topics in Mathematical Fluid Mechanics: Cetraro, Italy 2010, Editors: Hugo Beirão da Veiga, Franco Flandoli (C.I.M.E. Foundation Subseries)

Růžička, Michael

Galdi, Giovanni P.

Debussche, Arnaud

Seregin, Gregory

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