  We investigate long-range correlations (LRCs) induced by shear flow using the
molecular dynamics (MD) simulation. We observe the LRCs by comparing the MD
results with the linearized fluctuating hydrodynamics (LFH). We find that the
MD result has large finite-size effects, and it prevents the occurrence of LRCs
in small systems. We examine the finite-size effects using a sufficiently large
system consisting of more than ten million particles, and verify the existence
of shear-induced LRCs without ambiguity. Furthermore, we show that MD result is
quantitatively consistent with the LFH solution for the large system. As we
reduce the system size $L$ or increase the shear rate $\dot{\gamma}$, the
hydrodynamic description gradually breaks down in the long-wavelength region.
We define a characteristic wavenumber $k^{\rm vio}$ associated with the
breakdown and find the nontrivial scaling relations $k^{\rm vio} \propto
L^{-\omega}$ and $k^{\rm vio} \propto \dot{\gamma}$, where $\omega$ is an
exponent depending on $\dot{\gamma}$. These relations enable us to estimate the
finite-size effects in a larger-size simulation from a smaller system.
