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Blow-Up of Modified Navier--Stokes Equations in Nonhomogeneous Fourier Spaces
Abstract
We study the three-dimensional incompressible Navier--Stokes equations with a componentwise nonlinear damping term of the form α∑k=13 uk2m+1ek in Fourier and Fourier-- Gevrey spaces based on 𝒳0(ℝ3). 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 𝒳0(ℝ3).
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BibTeX
@misc{benameur2026blowup,
title = {{Blow-Up of Modified Navier--Stokes Equations in Nonhomogeneous Fourier Spaces}},
author = {Jamel Benameur and Lotfi Jlali},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32719},
eprint = {2609.32719},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32719},
}
RIS
TY - UNPB
TI - Blow-Up of Modified Navier--Stokes Equations in Nonhomogeneous Fourier Spaces
AU - Jamel Benameur
AU - Lotfi Jlali
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32719
UR - https://arxiv.org/abs/2609.32719
AB - We study the three-dimensional incompressible Navier--Stokes equations with a componentwise nonlinear damping term of the form α∑_k=1^3 u_k^2m+1e_k in Fourier and Fourier-- Gevrey spaces based on 𝒳^0(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 𝒳^0(ℝ^3).
ER -