Geodesic
The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes
Journal of the European Mathematical Society, Tome 15 (2013) no. 5, pp. 1629-1700

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We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region {r≤4t​}.
DOI : 10.4171/jems/400
Classification : 83-XX, 35-XX, 00-XX
Keywords: Kerr spacetime, wave equation, null condition, global existence 
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     author = {Jonathan Luk},
     title = {The null condition and global existence for nonlinear wave equations on slowly rotating {Kerr} spacetimes},
     journal = {Journal of the European Mathematical Society},
     pages = {1629--1700},
     publisher = {mathdoc},
     volume = {15},
     number = {5},
     year = {2013},
     doi = {10.4171/jems/400},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/400/}
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Jonathan Luk. The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes. Journal of the European Mathematical Society, Tome 15 (2013) no. 5, pp. 1629-1700. doi: 10.4171/jems/400

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