Year: 2026
Type: preprint
Abstract: We study the three-dimensional incompressible Navier--Stokes equations with a componentwise nonlinear damping term of the form $α\sum_{k=1}^3 u_k^{2m+1}e_k$ in Fourier and Fourier-- Gevrey spaces based on $\mathcal{X}^0(\mathbb{R}^3)$. We first establish local-in-time existence and uniqueness of solutions and obtain the corresponding unique maximal solutions. We then derive blow-up criteria in the Fourier--Gevrey framework, including an integral blow-up criterion in a weaker exponential weight. Moreover, we establish a quantitative lower bound for the solution near a possible finite maximal existence time. By iterating the loss of exponential weight, we finally obtain a corresponding lower bound in the unweighted Fourier space $\mathcal{X}^0(\mathbb{R}^3)$.
Source: arXiv (Cornell University)
Authors: Benameur, Jamel, Jlali, Lotfi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214736998