PreprintarXiv licencearXiv
Sharp Basic Velocity Estimates for the Plane Steady Navier--Stokes Equations through Vorticity
Abstract
We consider some new velocity estimates for general steady Navier-Stokes solutions in plane domains. Namely, we obtain some optimal estimates of the difference between mean values of the velocity over two concentric circles in terms of the L2-norm of the vorticity in the annulus between the circles. The sharpness of the estimates is demonstrated by some unexpected counterexamples.
Related
- Pressure estimates and classifications for steady H1loc-solutions to two-dimensional incompressible Euler equations
- Vorticity blowup in 2D compressible Euler equations
- Wasserstein regularity of vorticity solutions to the 2D Navier-Stokes equations
- Nonuniqueness of Solutions to 2D Incompressible Euler Equations with Unbounded Vorticity
- Global well-posedness of the 3D Navier-Stokes equations with helical L1 vorticity
BibTeX
@misc{korobkov2026sharp,
title = {{Sharp Basic Velocity Estimates for the Plane Steady Navier--Stokes Equations through Vorticity}},
author = {Mikhail Korobkov and Zhixiang Zhuang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30844},
eprint = {2609.30844},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30844},
}
RIS
TY - UNPB
TI - Sharp Basic Velocity Estimates for the Plane Steady Navier--Stokes Equations through Vorticity
AU - Mikhail Korobkov
AU - Zhixiang Zhuang
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30844
UR - https://arxiv.org/abs/2609.30844
AB - We consider some new velocity estimates for general steady Navier-Stokes solutions in plane domains. Namely, we obtain some optimal estimates of the difference between mean values of the velocity over two concentric circles in terms of the L^2-norm of the vorticity in the annulus between the circles. The sharpness of the estimates is demonstrated by some unexpected counterexamples.
ER -