On the Local Type I Conditions for the 3D Euler Equations

초록

We prove local non blow-up theorems for the 3D incompressible Euler equations under local Type I conditions. More specifically, for a classical solution of the 3D Euler equations, where is the ball with radius r and the center at x (0), if the limiting values of certain scale invariant quantities for a solution v(center dot, t) as are small enough, then does not blow-up at t = 0 in B(x (0), r).

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