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

Abstract

We study the fractional Navier-Stokes equations with cubic damping in the specific Lei-Lin-Gevrey space ${\mathcal{X}}_{a,\sigma }^0({\mathbb{R}}^3)$ (with $a\ge 0$ and $\sigma \ge 1$). 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 $\gamma =\frac{1}{2}$ of the usual Navier-Stokes system.

arXiv comment20 pages