2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70147We solve here the so called division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that semilinear wave equations which can be written as systems involving quadratic derivative non-linearities are globally well posed in (6+1) and higher dimensions for all regularities greater than the scaling. This paper is the first in a series of works where we discuss the global regularity properties of general non-linear wave equations for all spatial dimensions greater than or equal to 4.24 pages, 2 figuresAnalysis of PDEs35L05text