On local well-posedness of nonlinear dispersive equations with partially regular data

Youngwoo Koh, Yoonjung Lee, Ihyeok Seo

We revisit the local well-posedness theory of nonlinear Schrödinger and wave equations in Sobolev spaces $H^s$ and ${\dot{H}}^s$, $0<s\le 1$. The theory has been well established o…