Blow-up criterion of strong solutions to the Navier-Stokes equations in Besov spaces with negative indices

[摘要] A Holder type inequality in Besov spaces is established and applied to show that every strong solution u(t, x) on (0, T) of the Navier-Stokes equations can be continued beyond t > T provided that the vorticity w(t, x) is an element of L2/2-alpha(0, T; (B) over dot(infinity,infinity)(-alpha)(R-3)) boolean AND L2/1-alpha(0, T; (B) over dot(infinity,infinity)(-alpha)(R-3)) for 0 < alpha < 1. (C) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-01

[关键词] Navier-Stokes equations;Besov spaces;blow-up criterion;regularity of weak solutions