Existence of solutions to the nonstationary Stokes system in $H_{-μ}^{2,1}$, μ ∈ (0,1), in a domain with a distinguished axis. Part 1. Existence near the axis in 2d

W. M. Zajączkowski

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The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, ${v \cdot n ̅ |}_{S} = 0$ , S = ∂Ω in weighted $L_{p}$ -Sobolev spaces is proved. It is assumed that an axis L crosses Ω and the weight is a negative power function of the distance to the axis. The main part of the proof is devoted to examining solutions of the problem in a neighbourhood of L. The existence in Ω follows from the technique of regularization.

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Displaying similar documents to “Existence of solutions to the nonstationary Stokes system in H - μ 2 , 1 , μ ∈ (0,1), in a domain with a distinguished axis. Part 1. Existence near the axis in 2d”

Displaying similar documents to “Existence of solutions to the nonstationary Stokes system in $H_{- μ}^{2, 1}$ , μ ∈ (0,1), in a domain with a distinguished axis. Part 1. Existence near the axis in 2d”