In this paper, we establish a regularity criterion for solutions to the Navier-stokes equations, which is only related to one component of the velocity field. Let be a weak solution to the Navier-Stokes equations. We show that if any one component of the velocity field , for example , satisfies either
with and for some positive , then is regular on .
Submitted November 7, 2001. Published March 17, 2002.
Math Subject Classifications: 35Q30, 76D05.
Key Words: Navier-Stokes equations, weak solutions, regularity.
Show me the PDF file (265K), TEX file, and other files for this article.
| Cheng He |
Department of Mathematics, Faculty of Science
Rokko, Kobe, 657-8501, Japan
On leave from:
Academy of Mathematics and System Sciences,
Academia Sinica, Beijing, 100080, China.
Return to the EJDE web page