$L^2 $- DECAY OF SOLUTIONS OF THREE DIMENSIONAL INCOMPRESSIBLE MHD EQUATIONS: A MODIFIED APPROACH

SANJAY SARWE; SHRADDHA SADAVARTE; RAVI SARAYKAR

doi:10.5269/bspm.68618

$L^2 $- DECAY OF SOLUTIONS OF THREE DIMENSIONAL INCOMPRESSIBLE MHD EQUATIONS: A MODIFIED APPROACH

Auteurs-es

SANJAY SARWE DEPARTMENT OF MATHEMATICS, ST. FRANCIS DE SALES COLLEGE, NAGPUR - 440006, INDIA
SHRADDHA SADAVARTE Department of Mathematics, Suryodaya College of Engineering and Technology, Nagpur - 440027, India https://orcid.org/0009-0008-0748-3267
RAVI SARAYKAR Department of Mathematics, R.T.M. Nagpur University Campus, Nagpur - 440033, India. https://orcid.org/0000-0001-6619-9567

DOI :

https://doi.org/10.5269/bspm.68618

Résumé

In this paper, we adopt a recent and modified approach to prove $L^2$-decay properties of solutions of incompressible MHD equations following the methods in H. Sohr [“{\it The Navier-Stokes Equations: An Elementary Functional Analytic Approach}”, Birkhauser Advanced Texts, Birkhauser Verlag, Basel, 2001. ]
and Duong and Khai [TNU Journal of Science and Technology, Vol. 225 (02), 45-51 (2020) ]. Also, we compare our results with previously known results in the literature and find that our results (decay rate) are sharper than previously proven results. Last Theorem is an additional property of solutions of MHD equations, namely that they approach solution of homogeneous system as $t \to \infty$.

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Publié

2025-01-27

Numéro

Vol. 43 (2025)

Rubrique

Research Articles

Licence

When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).

The journal utilize the Creative Common Attribution (CC-BY 4.0).

Comment citer

SARWE, S., SADAVARTE, S., & SARAYKAR, R. (2025). $L^2 $- DECAY OF SOLUTIONS OF THREE DIMENSIONAL INCOMPRESSIBLE MHD EQUATIONS: A MODIFIED APPROACH. Boletim Da Sociedade Paranaense De Matemática, 43, 1-15. https://doi.org/10.5269/bspm.68618