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