Space-time regularity of the Koch & Tataru solutions to Navier-Stokes equations

In Koch & Tataru (2001), the authors have proved local and global well- posedness of the Navier-Stokes equations with small initial data u(0) is an element of BMO-1. And then the spatial analyticity of the Koch & Tataru solution stated as t(k/2)del(k)u is an element of X-T* for any positive integer k has been presented by Germain-Pavlovic'- Staffilani (2007), where X-T* is the space defined by Koch & Tataru (2001), (see also Definition 1.2). In this paper, we shall present the space-time regularity. More precisely, for any positive integer m, k, we have t(m+k/2) partial derivative(m)(t)del(k) u is an element of X-T*. (C) 2014 Elsevier Ltd. All rights reserved.