Interface Fluctuations, Burgers Equations, and Coarsening under Shear

We consider the interplay of thermal fluctuations and shear on the surface of the domains in various systems coarsening under an imposed shear flow. These include systems with nonconserved and conserved dynamics, and a conserved order parameter advected by a fluid whose velocity field satisfies the Navier-Stokes equation. In each case the equation of motion for the interface height reduces to an anisotropic Burgers equation. The scaling exponents that describe the growth and coarsening of the interface are calculated exactly in any dimension in the case of conserved and nonconserved dynamics. For a fluid-advected conserved order parameter we determine the exponents, but we are unable to build a consistent perturbative expansion to support their validity.