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A Hölder estimate for the trajectories of the Navier-Stokes equations
We study solutions to the Navier-Stokes equations in the class $L^\infty_t C^α_x$. Landau and Lifshitz [LL87] predicted that the Eulerian and Lagrangian temporal structure functions for turbulence exhibit $1/3$ and $1/2$ scaling laws, respectively. These laws were justified for the Euler equations i
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