On the Stokes semigroup in some non-Helmholtz domains

This paper shows that the Lp-Helmholtz decomposition is not necessary to establish the analyticity of the Stokes semigroup in C0,σ, the L∞-closure of the space of all compactly supported smooth solenoidal vector fields. In fact, in a sector-like domain for which the Lp-Helmholtz decomposition does not hold, the analyticity of the Stokes semigroup in C0,σ is proved.

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