The Navier-stokes Equations in the Critical Lebesgue Space
نویسنده
چکیده
We study regularity criteria for the d-dimensional incompressible Navier-Stokes equations. We prove in this paper that if u ∈ L ∞ Lxd((0, T ) × R ) is a Leray-Hopf weak solution, then u is smooth and unique in (0, T )× R. This generalizes a result by Escauriaza, Seregin and Šverák [5]. Additionally, we show that if T = ∞ then u goes to zero as t goes to infinity.
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تاریخ انتشار 2009