THE L ∞-STOKES SEMIGROUP IN EXTERIOR DOMAINS
Ken Abe, Yoshikazu Giga · Hokkaido University Collection of Scholarly and Academic Papers (Hokkaido University) · 2012
Abstract. The Stokes semigroup is extended to an analytic semigroup in spaces of bounded functions in an exterior domain with C3 boundary. Some of these spaces include vector fields non-decaying at the space infinity. Moreover, uniform bounds by a sup-norm of initial velocity are established in finite time for second spacial derivatives of velocity and also for gradient of pressure to the Stokes equations. 1. Introduction and