A Fuchsian viewpoint on the weak null condition

We analyze systems of semilinear wave equations in 3+1 dimensions whose associated asymptotic equation admit bounded solutions for suitably small choices initial data. Under this special case the weak null condition, which we refer to as prove existence these on neighborhoods spatial infinity under a data assumption. Existence is established using Fuchsian method. This method involves transforming into defined spacetime region. The then follows from an application theory developed [11]. This, turn, yields, by construction, original system neighborhood infinity.