The stationary Navier-Stokes equations in the scaling invariant Triebel-Lizorkin spaces. (Q2423438)

The author studies Navier-Stokes equation problems in homogeneous Triebel-Lizorkin spaces. First, he shows existence and uniqueness for small external forces, inspired by a paper by \textit{K. Kaneko, H. Kozono} and \textit{S. Shimizu} [``Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity'', Indiana Univ. Math. J. (to appear)]. Moreover, he considers the additional regularity of solutions, under some additional assumptions. The homogeneous Triebel-Lizorkin spaces are complete and, before the proofs the author points out that they have some important properties. The estimates for a para-product of functions, as well as some properties related to the Riesz transforms on the homogeneous Triebel-Lizorkin spaces, are recalled in the first part of the paper.