Infinite Time Blow-up Solutions to the Energy Critical Wave Maps Equation PDF Download
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Author: Mohandas Pillai
Publisher:
ISBN: 9781470474454
Category : Differential equations, Partial
Languages : en
Pages : 0
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Book Description
Author: Mohandas Pillai
Publisher:
ISBN: 9781470474454
Category : Differential equations, Partial
Languages : en
Pages : 0
Get Book
Book Description
Author: Mohandas Pillai
Publisher: American Mathematical Society
ISBN: 1470459930
Category : Mathematics
Languages : en
Pages : 254
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Author: Joachim Krieger
Publisher: European Mathematical Society
ISBN: 9783037191064
Category : Differential equations, Hyperbolic
Languages : en
Pages : 494
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Book Description
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 $\mathbb R^{2+1}_{t,x}$, 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 $M =\mathbb S^2$ 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.
Author: Hiroshi Kihara
Publisher: American Mathematical Society
ISBN: 1470465426
Category : Mathematics
Languages : en
Pages : 144
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Author: Roelof Bruggeman
Publisher: American Mathematical Society
ISBN: 1470465450
Category : Mathematics
Languages : en
Pages : 186
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Author: David A. Craven
Publisher: American Mathematical Society
ISBN: 147046702X
Category : Mathematics
Languages : en
Pages : 226
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Author: Agelos Georgakopoulos
Publisher: American Mathematical Society
ISBN: 1470467054
Category : Mathematics
Languages : en
Pages : 114
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Author: Olivier Bernardi
Publisher: American Mathematical Society
ISBN: 1470466996
Category : Mathematics
Languages : en
Pages : 188
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Author: Dieter Degrijse
Publisher: American Mathematical Society
ISBN: 1470467046
Category : Mathematics
Languages : en
Pages : 154
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Author: Pavel Galashin
Publisher: American Mathematical Society
ISBN: 1470467003
Category : Mathematics
Languages : en
Pages : 92
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