Existência global para a equação periódica e dispersiva de Hunter-Saxton

Abstract

In this master's thesis, we study the recent results about global existence for the integrable dispersive Hunter–Saxton equation in a periodic domain. Firstly, the local well-posedness of the Cauchy problem of the equation is established in $H^s(\mathbb{S}) $, $ s \geq 2 $, by applying the Kato method. Then, based on a sign-preserve property, a global existence result is obtained for the equation in $H^s(\mathbb{S}) $, $ s \geq 3$. Moreover, the obtained result is extended to some periodic nonlinear partial differential equations of second order of the general form.