Existence of solutions to the nonstationary Stokes system in , μ ∈ (0,1), in a domain with a distinguished axis. Part 2. Estimate in the 3d case
W. M. Zajączkowski (2007)
Applicationes Mathematicae
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We examine the regularity of solutions to the Stokes system in a neighbourhood of the distinguished axis under the assumptions that the initial velocity v₀ and the external force f belong to some weighted Sobolev spaces. It is assumed that the weight is the (-μ )th power of the distance to the axis. Let , , μ ∈ (0,1). We prove an estimate of the velocity in the norm and of the gradient of the pressure in the norm of . We apply the Fourier transform with respect to the variable along...