The coupling of the Schr\odinger equation with a Newtonian self-interaction field leads in the two-dimensional case to a Choquard equation with a logarithmic internal potential
$$
-\Delta u +u = \Bigl(\log \frac{1}{\vert \cdot \vert} \ast \vert u \vert^2\Bigr) u
$$
The divergence of latter logarithmic potential at infinity prevents the natural energy functional to be well-defined and smooth on the natural Sobolev space induced by the linear part of the equation. I will present a new relaxation scheme that Luca Battaglia and I have developped to construct solutions to this Choquard problem and some nondegeneracy result obtained in collaboration with Denis Bonheure and Silvia Cingolani.