Lower Bounds on the Blow-Up Rate of the Axisymmetric Navier–Stokes Equations II
Strain, Robert M.
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CitationChen, Chiun-Chuan, Robert M. Strain, Tai-Peng Tsai, and Horng-Tzer Yau. 2009. “Lower Bounds on the Blow-Up Rate of the Axisymmetric Navier–Stokes Equations II.” Communications in Partial Differential Equations 34 (3) (March 25): 203–232. doi:10.1080/03605300902793956.
AbstractConsider axisymmetric strong solutions of the incompressible Navier–Stokes equations in ℝ3 with non-trivial swirl. Let z denote the axis of symmetry and r measure the distance to the z-axis. Suppose the solution satisfies, for some 0 ≤ ε ≤ 1, |v (x, t)| ≤ C ∗ r −1+ε |t|−ε/2 for − T 0 ≤ t < 0 and 0 < C ∗ < ∞ allowed to be large. We prove that v is regular at time zero.
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