Tongkeun Chang, Kyungkeun Kang
Published 2021-10-14, updated 2022-04-15Version 2
We are concerned with local regularity of the solutions for the Stokes and Navier-Stokes equations near boundary. Firstly, we construct a bounded solution but its normal derivatives are singular in any $L^p$ with $1<p$ locally near boundary. On the other hand, we present criteria of solutions of the Stokes equations near boundary to imply that the gradients of solutions are bounded (in fact, even further H\"{o}lder continuous). Finally, we provide examples of solutions whose local regularity near boundary is optimal.
Regularity of Leray-Hopf solutions to Navier-Stokes equations (II)-Blow up rate with small L^2(R^3) data
Smoothness criteria for Navier-Stokes equations in terms of regularity along the steam lines
An H^1 setting for the Navier-Stokes equations: quantitative estimates
![QR code for arXiv:2110.07162 [math.AP]](http://oss.arxitics.com/images/favicon.svg)