Analyticity and asymptotics for the Stokes solutions in a weighted space

We first show the analyticity of Stokes operator in a weighted space L-gamma(p)(R-+(3)). We also show that the Hodge decomposition holds on L-gamma(p) (R-+(3)). Then, we estimate the asymptotic behavior of the Stokes solutions in space and time directions. For 1 < r < q < infinity, if t is large enough, then (integral(R3+)\u(x,t)\W-q(x)(gammaq)dx)(1/q) less than or equal to C/(t)(3/2)(1/r - 1/q) +1/2-gamma/2' where gamma is a constant with 0 less than or equal to y < 3/r' if w(x) = 1 + \x\, and 0 < y < 1/r' if w(x) = 1 + x(n). (C) 2002 Elsevier Science (USA). All rights reserved.