14 January 2014
The Maxwell equation is an intermediate linear model for Einstein's equation lying between the scalar wave equation and the linearised Einstein equation. This talk will present the 5 key estimates necessary to prove a uniform bound on an energy and a Morawetz integrated local energy decay estimate for the nonradiating part. The major obstacles, relative to the scalar wave equation are: that a scalar equation must be found for at least one of the components, since there is no known decay estimate directly at the tensor level; that the scalar equation has a complex potential; and that there are stationary solutions and, in the nonzero $a$ Kerr case, it is more difficult to project away from these stationary solutions. If time permits, some discussion of a geometric proof using the hidden symmetries will be given. This is joint work with L. Andersson and is arXiv:1310.2664.
- Partial Differential Equations Seminar