  We present a hybrid simulation method which allows one to study the dynamical
evolution of self-assembling (co)polymer solutions in the presence of
hydrodynamic interactions. The method combines an established dynamic density
functional theory for polymers that accounts for the nonlocal character of
chain dynamics at the level of the Rouse model, the external potential dynamics
(EPD) model, with an established Navier-Stokes solver, the Lattice Boltzmann
(LB) method. We apply the method to study the self-assembly of nanoparticles
and vesicles in two-dimensional copolymer solutions in a typical microchannel
Poiseuille flow profile. The simulations start from fully mixed systems which
are suddenly quenched below the spinodal line. In order to isolate effects
caused by walls, we use a reverse Poiseuille flow geometry with periodic
boundary conditions. We identify three stages of self assembly, i.e., initial
spinodal decomposition, particle nucleation, and particle growth (ripening). We
find that (i) In the presence of shear, the nucleation of droplets is delayed
by an amount roughly proportional to the shear rate, (ii) Shear flow greatly
increases the rates of particle fusions, (iii) in later stages of
self-assembly, stronger shear flows may induce irreversible shape
transformation {\em via} finger formation, in particular in vesicle systems.
The combination of these effects lead to an accumulation of particles close to
the center of the Poiseuille flow profile, and the polymeric matter has a
double peak distribution centered around the flow maximum.
