2009/10/02 by Jason Metcalfe, Christopher D. Sogge, Metcalfe, Jason +1
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.0910.0433
We study long time existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles. In particular, we obtain exterior domain analogs of the four dimensional results of Hörmander where the nonlinearity is permitted to depend on the solution not just its first and second derivatives. Previous proofs in exterior domains omitted this dependence as it did not mesh well with the energy methods in use.