Low-regularity local well-posedness for some dispersive equations

Dispersive partial differential equations (PDEs) describe how waves spread out over time, with different frequencies traveling at different speeds. These equations are fundamental in physics and engineering, modeling phenomena such as water waves, sound waves, and light propagation. A key challenge in studying nonlinear PDEs is determining their well-posedness—whether a unique solution exists satisfying initial conditions, and remains stable under perturbations. This thesis explores the local well-posedness of various dispersive PDEs, providing a rigorous mathematical analysis to understand their behavior.