Items related to Concentration Compactness for Critical Wave Maps (EMS...
Synopsis
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 semilinear 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, such as $mathbb R2+1t,x$, present particular technical difficulties. This class of wave maps has the additional important feature of being energy critical, 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 $M =mathbb S2$ as target. This monograph establishes that for $mathbb H$ as target the wave map evolution of any smooth data exists globally as a smooth function. While the authors restrict themselves 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. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
"synopsis" may belong to another edition of this title.
Search results for Concentration Compactness for Critical Wave Maps (EMS...
International Edition
Concentration Compactness for Critical Wave Maps
Published by
European Mathematical Society, Zurich, 2012
ISBN 10: 3037191066
ISBN 13: 9783037191064
New
Trade paperback
Seller: Aideo Books, San Marino, CA, U.S.A.
Seller rating 5 out of 5 stars
Trade paperback. Condition: 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. Seller Inventory # K6230001127
International Edition
Concentration Compactness for Critical Wave Maps (EMS Monographs in Mathematics)
Published by
U.S.A.: European Mathematical Society, 2012
ISBN 10: 3037191066
ISBN 13: 9783037191064
New
Soft cover
Seller: Sizzler Texts, SAN GABRIEL, CA, U.S.A.
Seller rating 5 out of 5 stars
Soft cover. Condition: New. Dust Jacket Condition: 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. Seller Inventory # ABE-16598407319