Recent developments in the Navier-Stokes problem
Author(s)
Bibliographic Information
Recent developments in the Navier-Stokes problem
（Research notes in mathematics, 431）
Chapman & Hall/CRC, c2002
Available at / 44 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
LEM||6||1||複本200003622406
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC21:515.353/L5412070559212
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Note
Bibliography: p. 383-390
Includes indexes
Description and Table of Contents
Description
The Navier-Stokes equations: fascinating, fundamentally important, and challenging,. Although many questions remain open, progress has been made in recent years. The regularity criterion of Caffarelli, Kohn, and Nirenberg led to many new results on existence and non-existence of solutions, and the very active search for mild solutions in the 1990's culminated in the theorem of Koch and Tataru that, in some ways, provides a definitive answer.
Recent Developments in the Navier-Stokes Problem brings these and other advances together in a self-contained exposition presented from the perspective of real harmonic analysis. The author first builds a careful foundation in real harmonic analysis, introducing all the material needed for his later discussions. He then studies the Navier-Stokes equations on the whole space, exploring previously scattered results such as the decay of solutions in space and in time, uniqueness, self-similar solutions, the decay of Lebesgue or Besov norms of solutions, and the existence of solutions for a uniformly locally square integrable initial value. Many of the proofs and statements are original and, to the extent possible, presented in the context of real harmonic analysis.
Although the existence, regularity, and uniqueness of solutions to the Navier-Stokes equations continue to be a challenge, this book is a welcome opportunity for mathematicians and physicists alike to explore the problem's intricacies from a new and enlightening perspective.
Table of Contents
Introduction. Some Results of Real Harmonic Analysis. A General Framework for Shift-Invariant Estimates for the Navier-Stokes Equations. Classical Existence Results for the Navier-Stokes Equations. New Approaches of Mild Solutions. Decay and Regularity Results for Weak and Mild Solutions. Local Energy Inequalities for the Navier-Stokes Equations on R3. Conclusion. References. Bibliography. Index Nominum. Index Rerum.
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