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期刊论文
Forward self-similar solutions of the fractional Navier-Stokes equations
Advances in Mathematics,2019,352(2):981–1043 | 2019年06月28日 | 10.1016/j.aim.2019.06.021
We study forward self-similar solutions to the 3-D Navier-Stokes equations with the fractional diffusion (−Δ)^α. First, we construct a global-time forward self-similar solutions to the fractional Navier-Stokes equations with 5/6 <α ≤1for arbitrarily large self-similar initial data by making use of the so called blow-up argument. Moreover, we prove that this so-lution is smooth in R^3×(0, +∞). In particular, when α =1, we prove that the solution constructed by Korobkov and Tsai (2016) [16]satisfies the decay estimate by establishing regu-larity of solution for the corresponding elliptic system, which implies this solution has the same properties as a solution which was constructed in Jia and Šverák (2014) [13].
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