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.

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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 -