Stabilization and L p –L q decay estimates

The goal of the paper is to derive Strichartz estimates for solutions to wave equations with time-dependent coefficients belonging to C^r, 2≤r≤2n+1, and generating an anisotropic speed of propagation. A stabilization condition for the coefficients is introduced. This condition allows to show the Log-effect in L^p–L^q estimates and explains in this way the loss of decay.