A sharp Lorentz-invariant Strichartz norm expansion for the cubic wave equation in $\mathbb{R}^{1+3}$

Abstract

We provide an asymptotic formula for the maximal Strichartz norm of small solutions to the cubic wave equation in Minkowski space. The leading coefficient is given by Foschi's sharp constant for the linear Strichartz estimate. We calculate the constant in the second term, which differs depending on whether the equation is focussing or defocussing. The sign of this coefficient also changes accordingly.