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arXiv · 2606.15189

Blow-up and uniqueness of Leray-Hopf solutions to forced Navier-Stokes equations

Giovanni Paolo Galdi·Filippo Gazzola
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Abstract

We prove the existence of forces and smooth initial data such that the associated Leray-Hopf solution of the 3D Navier-Stokes equations is unique, global-in-time, satisfies the energy equality, and has infinitely many (countable) blow-up instants. Different classes of forces and blow-up strengths are considered. All of them are sharp compared to the boundedness statements in literature. Our method also enables us to construct examples of blow-up for the forced 3D Euler equations.

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Giovanni Paolo Galdi, Filippo Gazzola. 2026-06-13. Blow-up and uniqueness of Leray-Hopf solutions to forced Navier-Stokes equations. https://arxiv.org/abs/2606.15189

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