By Dan-Andrei Geba,Manoussos G Grillakis
The wave maps approach is without doubt one of the most pretty and tough nonlinear hyperbolic platforms, which has captured the eye of mathematicians for greater than thirty years now. within the examine of its a variety of matters, corresponding to the well-posedness idea, the formation of singularities, and the steadiness of the solitons, as a way to receive optimum effects, one has to take advantage of tricky instruments coming not just from research, but additionally from geometry and topology. additionally, the wave maps procedure is not anything except the Euler–Lagrange process for the nonlinear sigma version, that is one of many primary difficulties in classical box theory.
One of the pursuits of our booklet is to provide an up to date and virtually self-contained evaluate of the most regularity effects proved for wave maps.
Another one is to introduce, to a large mathematical viewers, bodily stimulated generalizations of the wave maps procedure (e.g., the Skyrme model), that are super fascinating and tough of their personal right.
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