TY - JOUR
T1 - Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity
AU - Kaneko, Kenta
AU - Kozono, Hideo
AU - Shimizu, Senjo
N1 - Publisher Copyright:
Indiana University Mathematics Journal ©
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85113342798&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85113342798&partnerID=8YFLogxK
U2 - 10.1512/IUMJ.2019.68.7650
DO - 10.1512/IUMJ.2019.68.7650
M3 - Article
AN - SCOPUS:85113342798
SN - 0022-2518
VL - 68
SP - 857
EP - 880
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
IS - 3
ER -