Robinson, James C.Sadowski, WitoldSilva, Ricardo P. [UNESP]2013-09-302014-05-202013-09-302014-05-202012-11-01Journal of Mathematical Physics. Melville: Amer Inst Physics, v. 53, n. 11, p. 15, 2012.0022-2488http://hdl.handle.net/11449/25142Suppose that u(t) is a solution of the three-dimensional Navier-Stokes equations, either on the whole space or with periodic boundary conditions, that has a singularity at time T. In this paper we show that the norm of u(T - t) in the homogeneous Sobolev space (H)over dot(s) must be bounded below by c(s)t(-(2s-1)/4) for 1/2 < s < 5/2 (s not equal 3/2), where c(s) is an absolute constant depending only on s; and by c(s)parallel to u(0)parallel to((5-2s)/5)(L2)t(-2s/5) for s > 5/2. (The result for 1/2 < s < 3/2 follows from well-known lower bounds on blowup in Lp spaces.) We show in particular that the local existence time in (H)over dot(s)(R-3) depends only on the (H)over dot(s)-norm for 1/2 < s < 5/2, s not equal 3/2. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4762841]15engNavier-Stokes equationsArtigo10.1063/1.4762841WOS:000311964100019Acesso abertoWOS000311964100019.pdf