BESOV WE11-POSEDNESS FOR HIGH DIMENSIONAL NON-LINEAR WAVE EQUATIONS
BESOV WE11-POSEDNESS FOR HIGH DIMENSIONAL NON-LINEAR WAVE EQUATIONS
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Date
2003
Authors
Sterbenz, Jacob
Advisor
Machedon, Matei
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Abstract
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.