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Wave maps are the simplest wave equations taking their values in a Riemannian manifold (M,g). Their Lagrangian is the same as for the scalar equation, the only difference being that lengths are measured with respect to the metric g. By Noether's theorem, symmetries of the Lagrangian imply conservation laws for wave maps, such as conservation of energy. In coordinates, wave maps are given by a system of semillinear wave equations. Over the past 20 years important methods have emerged which address the problem of local and global wellposedness of this system. Due to weak dispersive effects, wave maps defined on Minkowski spaces of low dimensions present particular technical difficulties. This class of wave maps has the additional important feature of being energy critial, which refers to the fact that the energy scales exactly like the equation. Around 2000 Daniel Tataru and Terence Tao, building on earlier work of Klainerman–Machedon, proved that smooth data of small energy lead to global smooth solutions for wave maps from 2+1 dimensions into target manifolds satisfying some natural conditions. In contrast, for large data, singularities may occur in finite time for M =S^2 as target. This monograph establishes that for H as target the wave map evolution of any smooth data exists globally as a smooth function. While we restrict ourselves to the hyperbolic plane as target the implementation of the concentration-compactness method, the most challenging piece of this exposition, yields more detailed information on the solution. This monograph will be of interest to experts in nonlinear dispersive equations, in particular to those working on geometric evolution equations.
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Concentration Compactness for Critical Wave Maps
Verlag:
European Mathematical Society, Zurich, 2012
ISBN 10: 3037191066
ISBN 13: 9783037191064
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Anbieter: Aideo Books, San Marino, CA, USA
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Trade paperback. Zustand: New in new dust jacket. First edition. INTERNATIONAL EDITION. ***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service. 490 p. EMS Monographs in Mathematics. Audience: College/higher education. Bestandsnummer des Verkäufers K6230001127
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Internationale Ausgabe
Concentration Compactness for Critical Wave Maps (EMS Monographs in Mathematics)
Verlag:
U.S.A.: European Mathematical Society, 2012
ISBN 10: 3037191066
ISBN 13: 9783037191064
Neu
Soft cover
Anbieter: Sizzler Texts, SAN GABRIEL, CA, USA
Verkäuferbewertung 5 von 5 Sternen
Soft cover. Zustand: New. Zustand des Schutzumschlags: New. International Edition. **INTERNATIONAL EDITION** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments go through via USPS/UPS/DHL with tracking numbers. Great professional textbook selling experience and expedite shipping service. Bestandsnummer des Verkäufers ABE-16598407319
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