On the large time L∞-estimates of the Stokes semigroup in two-dimensional exterior domains

We prove that the Stokes semigroup is a bounded analytic semigroup on L-sigma(infinity) of angle pi/2 for twodimensional exterior domains. This result is an end point case of the L-p -boundedness of the semigroup for p is an element of ( 1 , infinity), 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. (C) 2021 Elsevier Inc. All rights reserved.