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arXiv · 2512.21312

Non-Algebraic Decay for Solutions to the Navier-Stokes Equations

Lorenzo Brandolese·Matthieu Pageard·Cilon F. Perusato
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Abstract

Around forty years ago, Michael Wiegner provided, in a seminal paper, sharp algebraic decay rates for solutions of the Navier--Stokes equations, showing that these solutions behave asymptotically like the solutions of the heat equation with the same data as $t\to+\infty$, in the $L^2$-norm, up to some critical decay rate. In the present paper, we close a gap that appears in the conclusion of Wiegner's theorem in the 2D case, for solutions with non-algebraic decay rate.

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Lorenzo Brandolese, Matthieu Pageard, Cilon F. Perusato. 2025-12-24. Non-Algebraic Decay for Solutions to the Navier-Stokes Equations. https://arxiv.org/abs/2512.21312

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