We consider the stationary problem of the Navier-Stokes equations in ℝn for n ≥ 3. We show existence, uniqueness, and regularity of solutions in the homogeneous Besov space Ḃp,q−1+n/p, which is the scaling invariant one. As a corollary of our results, a self-similar solution is obtained. For the proof, several bilinear estimates are established. The essential tool is based on the paraproduct formula and the imbedding theorem in homogeneous Besov spaces.
ASJC Scopus subject areas
- 数学 (全般)