Study of modified Navier–Stokes equations in Fourier spaces

Jamel Benameur; Lotfi Jlali; Jamel Benameur; Lotfi Jlali

doi:10.3934/math.2026525

AIMS Mathematics

2026, Volume 11, Issue 5: 12762-12779. doi: 10.3934/math.2026525

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Study of modified Navier–Stokes equations in Fourier spaces

Jamel Benameur ¹,
Lotfi Jlali ^{2
,
,}

1.
Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
2.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia

Received: 01 January 2026 Revised: 11 April 2026 Accepted: 29 April 2026 Published: 08 May 2026
MSC : 35Q30, 76D05, 76N10

In this paper, we study the modified Navier–Stokes equations with a damping term, assuming that the initial data $ u^0 $ satisfies $ \widehat{u^0}\in L^1(\mathbb{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.
- Navier–Stokes equations,
- global solution,
- local solution,
- Lei–Lin–Gevrey spaces
Citation: Jamel Benameur, Lotfi Jlali. Study of modified Navier–Stokes equations in Fourier spaces[J]. AIMS Mathematics, 2026, 11(5): 12762-12779. doi: 10.3934/math.2026525

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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 $ \widehat{u^0}\in L^1(\mathbb{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.

References

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