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Machedon, Matei Sterbenz, Jacob Digital Repository at the University of Maryland University of Maryland (College Park, Md) Mathematics 2019-09-25T16:49:43Z 2019-09-25T16:49:43Z 2003 https://doi.org/10.13016/ky8p-tfuz http://hdl.handle.net/1903/24912 Following work of Tataru, [13] and [11], we solve the division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that non-linear wave equations which can be written as systems involving equations of the form Φ = Φ∇Φ and Φ = |∇Φ|^2 are well-posed with scattering in (6+1) and higher dimensions if the Cauchy data are small in the scale invariant ℓ^1 Besov space B^sc,1. en_US BESOV WE11-POSEDNESS FOR HIGH DIMENSIONAL NON-LINEAR WAVE EQUATIONS Dissertation open.access