Local well-posedness for quadratic Schrödinger equations in ${\mathbf{R}}^{1+1}$: a normal form approach

Seungly Oh, Atanas Stefanov

For the Schrödinger equation $u_t+i u_{xx}=\nab^\be[u^2]$, $\be\in (0,1/2)$, we establish local well-posedness in $H^{\be-1+}$ (note that if $\be=0$, this matches, up to an endpoin…