  It was shown by the second author in (CPAA, 2019) for the biharmonic
Schr\"odinger equation and most recently by Himonas and Mantzavinos
(Nonlinearity, 2020) for 2D Schr\"odinger equation that Fokas method based
formulas are capable of defining weak solutions of associated nonlinear initial
boundary value problems (ibvps) below the Banach algebra threshold. In view of
these results, we revisit the theory of interior-boundary Strichartz estimates
for the Schr\"odinger equation posed on the right half line, considering both
Dirichlet and Neumann cases. Finally, we apply these estimates to obtain low
regularity solutions for the nonlinear Schr\"odinger equation (NLS) with
Neumann boundary condition and a coupled system of NLS equations defined on the
half line with Dirichlet/Neumann boundary conditions.
