  In this article, we consider a system of integro-differential equations in
L^2(R, R^N), which contains the logarithmic Laplacian in the presence of
transport terms. The linear operators associated with the system satisfy the
Fredholm property. By virtue of a fixed point technique, we demonstrate the
existence of solutions. We emphasize that the discussion is more complicated
than that of the scalar situation as there are more cumbersome technicalities
to overcome.
