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arXiv · 2508.01009

The structure of weak solutions to the Navier-Stokes equations

Zachary Bradshaw·Igor Kukavica
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Abstract

The existence of superfluous solutions to the Navier-Stokes equations in the whole space implies that not all solutions with uniformly locally bounded energy satisfy a useful local pressure expansion. We prove that every weak solution in a parabolic uniformly local $L^2$ class can be obtained as a transgalilean transformation of a solution satisfying the local pressure expansion in a distributional sense. This gives a powerful representation theorem for a large class of solutions. We use this structure to obtain a sufficient condition for the local pressure expansion.

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Zachary Bradshaw, Igor Kukavica. 2025-08-01. The structure of weak solutions to the Navier-Stokes equations. https://arxiv.org/abs/2508.01009

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