### arXiv:math/9811161 [math.AP]AbstractReferencesReviewsResources

#### Global regularity of the Navier-Stokes equation on thin three dimensional domains with periodic boundary conditions

Published 1998-11-27, updated 1999-12-03Version 2

This paper gives another version of results due to Raugel and Sell, and similar results due to Moise, Temam and Ziane, that state the following: the solution of the Navier-Stokes equation on a thin 3 dimensional domain with periodic boundary conditions has global regularity, as long as there is some control on the size of the initial data and the forcing term, where the control is larger than that obtainable via ``small data'' estimates. The approach taken is to consider the three dimensional equation as a perturbation of the equation when the vector field does not depend upon the coordinate in the thin direction.

**Comments:**Also available at http://math.missouri.edu/~stephen/preprints

**Journal:**Electronic J. Differential Equations, 1999, (1999), no. 11, 1-19

**Keywords:**periodic boundary conditions, dimensional domain, global regularity, navier-stokes equation, similar results

**Tags:**journal article

Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data

arXiv:0901.4359 [math.AP] (Published 2009-01-28)

Global regularity of solutions to systems of reaction-diffusion with Sub-Quadratic Growth in any dimension

arXiv:1609.03231 [math.AP] (Published 2016-09-11)

On the $L^p$ regularity of solutions to the generalized Hunter-Saxton system