Analyticity and asymptotics for the Stokes solutions in a weighted space ✩

We first show the analyticity of Stokes operator in a weighted space L pγ (R3 +). We also show that the Hodge decomposition holds on L pγ (R3+ ). Then, we estimate the asymptotic behavior of the Stokes solutions in space and time directions. For 1 < r q <∞, if t is large enough, then R3 + |u(x, t )|qω(x)γq dx 1/q C t (3/2)(1/r−1/q)+1/2−γ/2 , where γ is a constant with 0 γ < 3/r if ω(x) = 1 + |x|, and 0 γ < 1/r if ω(x) = 1 + xn.  2002 Elsevier Science (USA). All rights reserved.