On the Stochastic Regularization of 3D Euler Equations Through Random Diffusion

Mohamed Toumlilin

doi:10.32323/ujma.1815714

On the Stochastic Regularization of 3D Euler Equations Through Random Diffusion

Abstract

In this paper, we consider 3D stochastic incompressible Euler equations perturbed by a multiplicative noise term acting as a random diffusion. By introducing a random field to the diffusion coefficient and applying the Itô integral, we show that this noise induces a mathematical structure analogous to the Navier-Stokes equations. We establish local well-posedness through a contraction argument and a priori estimates for these stochastic parabolic equations. In addition, we show the global well-posedness results for small initial data belonging to Gevrey-type Fourier-Bessel potential spaces with high probability.

Keywords

Stochastic equation, Well-posedness, Random diffusion

References

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Details

Primary Language

English

Subjects

Partial Differential Equations

Journal Section

Research Article

Authors

Mohamed Toumlilin ^*
0000-0002-1039-4977
Morocco

Early Pub Date

June 12, 2026

Publication Date

-

Submission Date

November 2, 2025

Acceptance Date

June 7, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.32323/ujma.1815714

IZ

https://izlik.org/JA89RB94HL

APA

Toumlilin, M. (2026). On the Stochastic Regularization of 3D Euler Equations Through Random Diffusion. Universal Journal of Mathematics and Applications, Advanced Online Publication. https://doi.org/10.32323/ujma.1815714

AMA

1.Toumlilin M. On the Stochastic Regularization of 3D Euler Equations Through Random Diffusion. Univ. J. Math. Appl. 2026;(Advanced Online Publication). doi:10.32323/ujma.1815714

Chicago

Toumlilin, Mohamed. 2026. “On the Stochastic Regularization of 3D Euler Equations Through Random Diffusion”. Universal Journal of Mathematics and Applications, no. Advanced Online Publication. https://doi.org/10.32323/ujma.1815714.

EndNote

Toumlilin M (June 1, 2026) On the Stochastic Regularization of 3D Euler Equations Through Random Diffusion. Universal Journal of Mathematics and Applications Advanced Online Publication

IEEE

[1]M. Toumlilin, “On the Stochastic Regularization of 3D Euler Equations Through Random Diffusion”, Univ. J. Math. Appl., no. Advanced Online Publication, June 2026, doi: 10.32323/ujma.1815714.

ISNAD

Toumlilin, Mohamed. “On the Stochastic Regularization of 3D Euler Equations Through Random Diffusion”. Universal Journal of Mathematics and Applications. Advanced Online Publication (June 1, 2026). https://doi.org/10.32323/ujma.1815714.

JAMA

1.Toumlilin M. On the Stochastic Regularization of 3D Euler Equations Through Random Diffusion. Univ. J. Math. Appl. 2026. doi:10.32323/ujma.1815714.

MLA

Toumlilin, Mohamed. “On the Stochastic Regularization of 3D Euler Equations Through Random Diffusion”. Universal Journal of Mathematics and Applications, no. Advanced Online Publication, June 2026, doi:10.32323/ujma.1815714.

Vancouver

1.Mohamed Toumlilin. On the Stochastic Regularization of 3D Euler Equations Through Random Diffusion. Univ. J. Math. Appl. 2026 Jun. 1;(Advanced Online Publication). doi:10.32323/ujma.1815714