Regularity of Leray-hopf Solutions to Navier-stokes Equations (ii)–blow up Rate with Small L(r) Data
نویسندگان
چکیده
where u and p denote the unknown velocity and pressure of incompressible fluid respectively. In this paper, we estimate the upper bound of blow up rate for the Navier-Stokes equations. Main Theorem. There is δ > 0 such that if ‖u0‖L2(R3) ≤ δ, and if u is a LerayHopf solution to the problem (1.1) and blow up at t = T , then for any small ǫ > 0, there is t0 ∈ (0, T ), such that (1.2) ‖u(t)‖L∞(R3) ≤ ǫ (T − t)1/2 , for all t ∈ (t0, T ).
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