BESOV WE11-POSEDNESS FOR HIGH DIMENSIONAL NON-LINEAR WAVE EQUATIONS

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.

Department dc:contributor.department

Mathematics

Year dc:date.issued

2003

Author dc:creator

• Sterbenz, Jacob

Advisor dc:contributor.advisor

• Machedon, Matei

Language dc:language.iso

en_US

Identifier

https://doi.org/10.13016/ky8p-tfuz

OAI identifier oai:identifier

oai:drum.lib.umd.edu:1903/24912