PreprintarXiv licencearXiv
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 𝒳0a,σ(ℝ3) (with a≥0 and σ≥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 γ=1/2 of the usual Navier-Stokes system.
Related
- On the stability of solutions to the 3-D anisotropic Navier-Stokes equations in the critical space
- Ground state solutions for fractional p-Laplace equations with mixed nonlinearities in the critical and subcritical cases
- Asymptotic profiles for solutions to the incompressible Navier-Stokes equations in the critical Fourier-Herz spaces
- Critical fractional p-Hardy Sobolev equations: Global compactness and multiplicity of positive solutions
- Critical semilinear damped wave equations beyond moduli of continuity
BibTeX
@misc{donato2026solutions,
title = {{On solutions for damped fractional Navier-Stokes equations in a critical Lei-Lin-Gevrey space}},
author = {Bruno S. Donato and Wilberclay G. Melo and Thyago S. R. Santos},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32583},
eprint = {2609.32583},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32583},
}
RIS
TY - UNPB
TI - On solutions for damped fractional Navier-Stokes equations in a critical Lei-Lin-Gevrey space
AU - Bruno S. Donato
AU - Wilberclay G. Melo
AU - Thyago S. R. Santos
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32583
UR - https://arxiv.org/abs/2609.32583
AB - We study the fractional Navier-Stokes equations with cubic damping in the specific Lei-Lin-Gevrey space 𝒳^0_a,σ(ℝ^3) (with a≥0 and σ≥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 γ=1/2 of the usual Navier-Stokes system.
ER -