Sverak's conjecture on isolated singularities of stationary Navier–Stokes flows

Let uu be a solution of the stationary Navier–Stokes equations with zero force in R3{0}\mathbb{R}^3\setminus\{0\} satisfying the bound

u(x)Cx|u(x)|\leq \frac{C_*}{|x|}

for some C>0C_*>0. A Landau-solution conjecture. Then uu is a Landau solution.

This conjecture asks whether every stationary Navier–Stokes flow in three-dimensional punctured space with the critical pointwise bound is one of the explicit Landau solutions. The surrounding discussion states that the analogous classification of discretely self-similar solutions with large CC_* is unknown, while the result proved in the paper establishes the conclusion under the assumptions of its main theorem.

Sources & referencesView supporting material

Primary source

Hideyuki Miura and Tai-Peng Tsai, “Point singularities of 3D stationary Navier-Stokes flows”, arXiv:0810.2004 (2009).

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