Abstract
The two-dimensional Stokes IBVP on (0,T)times Omega is investigated under the assumptions that Omega subset {mathbb {R}}^2 is a smooth exterior domain, the initial datum v_0 belongs to L^infty (Omega ) and (v_0,nabla phi )=0 for all phi in L^1_{ell oc}(Omega ) with nabla phi in L^1(Omega ). The well-posedeness in L^infty ((0,T)times Omega ) and the maximum modulus theorem are achieved, in particular one deduces that the Stokes semigroup on L^infty (Omega ) is a bounded analytic semigroup.
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