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Research Article | Open Access

Study of modified Navier–Stokes equations in Fourier spaces

Jamel Benameur1, Lotfi Jlali2( )
Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
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Abstract

In this paper, we study the modified Navier–Stokes equations with a damping term, assuming that the initial data u 0 satisfies u 0 ^ ∈ L 1 ( R 3 ). We establish the existence and uniqueness of a local solution, together with a blow-up criterion in the case where the maximal time of existence is finite. The analysis relies on standard techniques from Fourier analysis.

Keywords

Navier–Stokes equationsglobal solutionlocal solutionLei–Lin–Gevrey spaces
CLC number: 35Q30, 76D05, 76N10

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AIMS Mathematics
Volume 11 Issue 5,
May 2026
Pages 12762-12779
DOI: 10.3934/math.2026525

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Benameur J, Jlali L. Study of modified Navier–Stokes equations in Fourier spaces. AIMS Mathematics, 2026, 11(5): 12762-12779. https://doi.org/10.3934/math.2026525

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Received: 01 January 2026
Revised: 11 April 2026
Accepted: 29 April 2026
Published: 15 May 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)