We are interested in the three-dimensional quasilinear wave equations with null condition. Global existence and pointwise decay for this model have been proved in the celebrated works of Klainerman \cite{ Klainerman86} and Christodoulou \cite{ Christodoulou86} for small smooth initial data. In this work, we illustrate the precise pointwise asymptotic behavior of the solutions for initial data posed on a hyperboloid and show that the decay rate $v^{ -1}u^{ -1}$ is optimal for a generic set of initial data.
Categories: math.AP