A commuting vectorfields approach to Strichartz-type inequalities and applications to quasi-linear wave equations (Q2725505)

The principal aim of this paper is to point out how, first for the wave equation on flat (Minkowski) space, (i) the Klainerman-Sobolev inequality implies the dispersive inequality, and (ii) the dispersive inequality implies the Strichartz estimate (without using the explicit solution formula in Fourier space). A variation of this approach is then used on a curved background to re-derive results related to those of H. F.~Smith, Bahouri and Chemin, and Tataru regarding wave equations \((-\partial_t^2+\sum_{i, j} h^{ij}\partial_i\partial_j)\varphi=0\) for metric coefficients \(h^{ij}\) of low regularity.