The purpose of this erratum is to correct some mistakes of Remark 1, Lemma 1 and their consequences in the paper [Arch Rational Mech Anal 193 (2009) 117–152]. The major contribution of the paper is to establish existence and regularity of very weak solutions in Lq( ) of the Dirichlet problem (NS) for the stationary Navier–Stokes equations with arbitrarily large boundary data g in W−1/q,q(∂ ). In particular, it is shown in Theorem 1, the main existence result, that there exists at least one very weak solution u ∈ Lq0( ) of (NS) in the sense of Definition 1 for the data f, k and g satisfying the very weak regularity (1). The proof of Theorem 1 is complete. Theorems 2 and 3, the main regularity results, are also correct. So are the corresponding results for the linear problems, i.e., Theorems 7, 9 and 10. However, due to the very weak regularity of f and k, the solution u neither satisfies (NS) in the usual distribution sense, nor does it have a well-defined trace, which contradicts the assertions in Remarks 2 and 3. In fact, Remarks 2 and 3 are wrong and should be corrected by imposing a stronger regularity assumption on f and k. Let X and Y be Banach spaces. Assume that X ↪→ Y , i.e., X ⊂ Y , and that there is a constant C > 0 such that ||x ||Y C ||x ||X for all x ∈ X . Then the restriction of each f ∈ Y ′ to X , denoted f |X , is a bounded linear functional on X ′ with the norm bounded by C || f ||Y ′ . Consider the space Y ′|X = { f |X : f ∈ Y ′} equipped with the quotient norm