Forward discretely self-similar solutions of the Navier-Stokes equations II

2015/10/26 by Bradshaw, Zachary, Tsai, Tai-Peng · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.07504

Abstract

For any discretely self-similar, incompressible initial data v₀ which satisfies ‖v₀ ‖_{L³w(\mathbb R³)}≤ c₀ where c₀ is allowed to be large, we construct a forward discretely self-similar local Leray solution in the sense of Lemarié-Rieusset to the 3D Navier-Stokes equations in the whole space. No further assumptions are imposed on the initial data; in particular, the data is not required to be continuous or locally bounded on \mathbb R³∖ \0\. The same method is used to construct self-similar solutions for any -1-homogeneous initial data in L³_w.

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• Time asymptotics, time regularity and separation rates for Navier-Stokes flows in supercritical solution classes

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