Space Analyticity for the Navier–Stokes and Related Equations with Initial Data inLp

We introduce a method of estimating the space analyticity radius of solutions for the Navier–Stokes and related equations in terms ofLpandL∞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.