Ordering of the lamellar phase under a shear flow

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The dynamics of a system quenched into a state with lamellar order and subject to an uniform shear flow is solved in the large-N limit. The description is based on the Brazovskii free-energy and the evolution follows a convection-diffusion equation. Lamellae order preferentially with the normal along the vorticity direction. Typical lengths grow as γt⁵/⁴ (with logarithmic corrections) in the flow direction and logarithmically in the shear direction. Dynamical scaling holds in the two-dimensional case while it is violated in D=3.