Event № 324
I present a new approach to classify the asymptotic behavior of certain types of wave equations, supercritical and others, with large initial data. In some cases, as for Nirenberg type equations, a fairly complete classification of the solutions (finite time blowup or global existence and scattering) is proved.
New results are obtained for the well known monomials wave equations in the sub/critical/super critical cases.
This approach, developed jointly with M. Beceanu, is based on a new decomposition into incoming and outgoing waves for the wave equation, and the positivity of the fundamental solution of the wave equation in three dimensions.