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arXiv · 2609.32583

On solutions for damped fractional Navier-Stokes equations in a critical Lei-Lin-Gevrey space

Bruno S. Donato·Wilberclay G. Melo·Thyago S. R. Santos
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Abstract

We study the fractional Navier-Stokes equations with cubic damping in the specific Lei-Lin-Gevrey space $\mathcal{X}^0_{a,σ}(\mathbb{R}^3)$ (with $a\geq0$ and $σ\geq1$). We establish local and small-data global well-posedness, quantitative blow-up criteria, Gevrey loss-of-radius estimates, and perturbative stability in the critical endpoint case $γ=\frac12$ of the usual Navier-Stokes system.

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Bruno S. Donato, Wilberclay G. Melo, Thyago S. R. Santos. 2026-09-26. On solutions for damped fractional Navier-Stokes equations in a critical Lei-Lin-Gevrey space. https://arxiv.org/abs/2609.32583

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