Findings from University of California Provide New Insights into General Mathematics
2012 APR 17 - (VerticalNews.com) -- "Let v be a solution of the axially symmetric Navier-Stokes equation. We determine the structure of a certain (possible) maximal singularity of v in the following sense," researchers in Riverside, California report.
"Let (x(0); t(0)) be a point where the flow speed Q(0) =vertical bar v(x(0); t(0))vertical bar is comparable with the maximum flow speed at and before time t(0). We show, after a space-time scaling with the factor Q(0) and the center (x(0); t(0)), that the solution is arbitrarily close in C-local(2,1,alpha) norm to a nonzero constant vector in a fixed parabolic cube, provided that r(0)Q(0) is sufficiently large. Here r(0) is the distance from x(0) to the z axis. Similar results are also shown to be valid if vertical bar r(0) v(x(0); t(0))vertical bar is comparable with the maximum of vertical bar r v(x, t)vertical bar at and before time t(0)," wrote Z. Lei and colleagues, University of California.
The researchers concluded: "This mirrors a numerical result of Hou for the Euler equation: there exists a certain 'calm spot' or depletion of vortex stretching in a region of high flow speed."
Lei and colleagues published their study in Pacific Journal of Mathematics (Structure Of Solutions Of 3d Axisymmetric Navier-stokes Equations Near Maximal Points. Pacific Journal of Mathematics, 2011;254(2):335-344).
For additional information, contact Z. Lei, University of California, Dept. of Math, Riverside, CA 92521, United States.
Publisher contact information for the Pacific Journal of Mathematics is: Pacific Journal Mathematics, PO Box 4163, Berkeley, CA 94704-0163, USA.
Keywords: City:Riverside, State:California, Country:United States, Region:North and Central America, General Mathematics
This article was prepared by VerticalNews Mathematics editors from staff and other reports. Copyright 2012, VerticalNews Mathematics via VerticalNews.com.