By Dan-Andrei Geba,Manoussos G Grillakis
The wave maps process is among the most pretty and hard nonlinear hyperbolic structures, which has captured the eye of mathematicians for greater than thirty years now. within the examine of its quite a few concerns, reminiscent of the well-posedness concept, the formation of singularities, and the soundness of the solitons, so as to receive optimum effects, one has to exploit tricky instruments coming not just from research, but in addition from geometry and topology. in addition, the wave maps approach 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 targets of our publication is to offer an updated and nearly self-contained review of the most regularity effects proved for wave maps.
Another one is to introduce, to a large mathematical viewers, bodily prompted generalizations of the wave maps method (e.g., the Skyrme model), that are tremendous fascinating and tough of their personal right.
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