# Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity

@article{Kaneko2019StationaryST, title={Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity}, author={Kenta Kaneko and Hideo Kozono and Senjo Shimizu}, journal={Indiana University Mathematics Journal}, year={2019} }

We consider the stationary problem of the Navier-Stokes equations in R for n ≥ 3. We show existence, uniqueness and regularity of solutions in the homogeneous Besov space Ḃ −1+np p,q 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. Introduction. Let us consider the…

## 13 Citations

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### Well-Posedness and Ill-Posedness Problems of the Stationary Navier–Stokes Equations in Scaling Invariant Besov Spaces

- Materials ScienceArchive for Rational Mechanics and Analysis
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