(Nazarbayev University School of Science and Technology, 2019-08-07) Biyar, Magzhan; da Silva, Daniel Oliveira; Castro Castilla, Alejandro Javier
We prove that the Cauchy problem for a transport equation with algebraic nonlinearity of
degree p with initial data in Gevrey spaces is locally well-posed. In particular, we show that
the analyticity of solutions persists for a short time and we derive a sufficient condition for
solutions to be analytic for all times.