Space analyticity for the Navier-Stokes and related equations with initial data in Lp

We introduce a method of estimating the space analyticity radios of solutions for the Navier-Stokes and related equations in terms of L-p and L-infinity norms of the initial data. The method enables us to express the space analyticity radius for 3D Navier-Stokes equations in terms of the Reynolds number of the flow. Also, for the Kuramoto-Sivashinsky equation, we give a partial answer to a conjecture that the radius of space analyticity on the attractor is independent of the spatial period. (C) 1998 Academic Press.