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The wave maps equation. (English) Zbl 1065.35199

The author deals with the wave maps equation. This is the simplest geometric nonlinear wave equation, which provides an excellent set up where one can begin the study of nonlinear wave interactions. Moreover, the wave maps arise in the analysis of more difficult hyperbolic Yang-Mills equations either as special cases or as equations for certain families of gauge transformations. They arise as well in general relativity for spacetimes with two Killing vector fields. The author presents a survey of the ideas and methods related to wave maps and discusses open problems as well.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35Q75 PDEs in connection with relativity and gravitational theory
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