Abstract
We prove that the Stokes semigroup is a bounded analytic semigroup on Lσ∞ of angle π/2 for two-dimensional exterior domains. This result is an end point case of the Lp-boundedness of the semigroup for p∈(1,∞), established by Borchers and Varnhorn (1993). The proof is based on the non-existence result of bounded steady flows (the Stokes paradox) and some asymptotic formula for the net force of the Stokes resolvent.
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