Global Regularity of the Navier-Stokes Equation on Thin Three-dimensional Domains with Periodic Boundary Conditions
Date
1999-04-14
Authors
Montgomery-Smith, Stephen
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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 three-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.
Description
Keywords
Navier-Stokes equation, Thin domain
Citation
Montgomery-Smith, S. (1999). Global regularity of the Navier-Stokes equation on thin three-dimensional domains with periodic boundary conditions. <i>Electronic Journal of Differential Equations, 1999</i>(11), pp. 1-19.
Rights
Attribution 4.0 International