  We analytically study coarsening dynamics in a system with nonconserved
scalar order parameter, when a uniform time-independent shear flow is present.
We use an anisotropic version of the Ohta-Jasnow-Kawasaki approximation to
calculate the growth exponents in two and three dimensions: for d=3 the
exponents we find are the same as expected on the basis of simple scaling
arguments, that is 3/2 in the flow direction and 1/2 in all the other
directions, while for d=2 we find an unusual behavior, in that the domains
experience an unlimited narrowing for very large times and a nontrivial
dynamical scaling appears. In addition, we consider the case where an
oscillatory shear is applied to a two-dimensional system, finding in this case
a standard t^1/2 growth, modulated by periodic oscillations. We support our
two-dimensional results by means of numerical simulations and we propose to
test our predictions by experiments on twisted nematic liquid crystals.
