Recent developments in the Navier-Stokes problem - Rilegato

Lemarie-Rieusset, Pierre Gilles

Rilegato

ISBN 10: 1584882204 ISBN 13: 9781584882206

Casa editrice: CRC Press, 2002

Riassunto

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.

Su questo libro

Informazioni sull'autore

Pierre Gilles Lemarie-Rieusset

Dalla quarta di copertina

Despite their importance and the amount of research published on the theory of the Navier-Stokes equations, some very elementary and fundamental questions remain unanswered. In this book, the author explores two main topics: the search for mild solutions using the tools of real harmonic analysis, and the 1982 regularity criterion of Caffarelli et al., which has produced many results on the existence or non-existence of solutions. The book includes a self-contained introduction to real harmonic analysis, addresses both strong solutions by direct methods and weak solutions by indirect methods, and presents new tools, including Besov spaces and wavelets.

Dettagli dell'edizione

• Editore: CRC Press
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 1584882204
• ISBN 13: 9781584882206
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 408
• Contatto del produttore: Taylor and Francis, GPSR Taylor and Francis; gpsr@taylorandfrancis.com; ; Taylor & Francis Verlag GmbH, Kaufingerstraße 24; München; 80331; Germania