[Differential Equations II] Final Report

In this report, we study the global existence of solutions to nonlinear dispersive wave equations \begin{eqnarray*}\partial_t^2 u + \frac{1}{\rho^2} |\partial_x|^{2\rho} u &=& \lambda |\partial_t u |^{p-1} \partial_t u\end{eqnarray*} in one space dimension where $0 < \rho \leqslant 2$, $\rho \neq … Continue reading