B. Pausader

A Physical-Space Approach to Modified Scattering for the 3D Hartree Equation: Full-Space and Robin Half-Space

We prove global well-posedness and modified scattering for the three-dimensional Hartree equation for small data in $H^{0,k}$, with $k>\frac12$ on $\mathbb R^3$ and $k=1$ on the half-space $\mathbb R^3_+$ with a real Robin boundary condition. For these data, the nonlinear and asymptotic analysis is carried out entirely...