Abstract
In this paper, we study the steady-state Navier Stokes equations in R-3. First, we establish the existence of very weak solution in L-p (R-3) with 3/2 < p < + infinity under smallness conditions on the data. A uniqueness result is also given in case the data belong to L-r(R-3) boolean AND L-3/2 (R-3) with 3/2 < r < 3. We also discuss the case where the data are not necessarily small. In particular, these results enhance those obtained by Bjorland et al. (Commun Partial Differ Equ 26:216-246. 2011), and are in agreement with those obtained by Kim and Kozono (3 Math Anal Appl. 395(2):486-195, 2012). Second, we prove a result of existence and uniqueness of weak solution in the weighted Sobolev space W-0(1,p) (R-3) boolean AND W-0(1,3/2) (R-3) in case of small external forces given by divF with F is an element of L-p (R-3) boolean AND L-3/2 (R-3) and 1 < p < 3.