On the Well-Posedness for the 3-D Micropolar Fluid System in Critical Fourier-Besov-Morrey Spaces

Authors

  • Dr. Fatima OUIDIRNE

Keywords:

Finite difference, mathematical induction, integral order, positive powers, arithmetic progression., reproductive property., 3-D micropolar fluid system, Fourier-Besov-Morrey spaces, well-posedness.

Abstract

In the present paper, we study the Cauchy problem of the incompressible micropolar fluid system in R3. We show that this problem is locally well-posed in Fourier-Besov-Morrey spaces.

References

A. Azanzal, A. Abbassi, C. Allalou (2021) On the Cauchy problem for the fractional drift-diffusion system in critical Fourier-Besov-Morrey spaces. p-28.

A. Azanzal, A. Abbassi, C. Allalou (2021) Existence of Solutions for the Debye-Hückel System with Low Regularity Initial Data in Critical Fourier-Besov-Morrey Spaces. 21, 367-380.

A. Azanzal, A. Abbassi, C. Allalou, S. Melliani (2021) Well-posedness and blow-up of solutions for the 2D dissipative quasi-geostrophic equation in critical Fourier-Besov-Morrey spaces. https://doi.org/10.1007/s41808-021-00140-x

A. Azanzal, C. Allalou, A. Abbassi (2021) Well-posedness and analyticity for generalized Navier-Stokes equations in critical Fourier-Besov-Morrey spaces.

Q. Chen, C. Miao (2012) Global well-posedness for the micropolar fluid system in critical Besov spaces. 252(3), 2698-2724.

B. Dong, J. Li, J. Wu (2017) Global well-posedness and large-time decay for the 2D micropolar equations. 262, 3488-3523.

A.C. El Baraka, M. Toumlilin (2019) Uniform well-Posedness and stability for fractional Navier-Stokes Equations with Coriolis force in critical Fourier-Besov-Morrey Spaces. (1), 70-89.

A.C. Eringen (1966) Theory of micropolar fluids. 16, 1-18.

L.C. Ferreira, E.J. Villamizar-Roa (2007) Micropolar fluid system in a space of distributions and large time behavior. 332(2), 1425-1445.

L.C. Ferreira, L.S. Lima (2014) Self-similar solutions for active scalar equations in Fourier-BesovMorrey spaces. 175(4), 491-509.

G.P. Galdi, S. Rionero (1977) A note on the existence and uniqueness of solutions of the micropolar fluid equations. 15, 105-108.

H. Inoue, Matsuura M. Ôtani (2003) Strong solutions of magneto-micropolar fluid equation. 439-448.

Z. Lei, F. Lin (2011) Global mild solutions of Navier-Stokes equations. 64(9), 1297-1304.

P.G. Lemarié-Rieusset (2012) The role of Morrey spaces in the study of Navier-Stokes and Euler equations. 3, 62-93.

G. Lukaszewicz (1988) On nonstationary flows of asymmetric fluids. 12, 83-97.

F. Ouidirne, H. Srhiri, C. Allalou, M. Oukessou Global existence for the 3-D generalized micropolar fluid system in critical Fourier-Besov spaces with variable exponents. 23(3), 338-347.

H. Srhiri, F. Ouidirne, C. Allalou, K. Hilal (2023) Well-posedness and stability of solutions for the 3-D generalized micropolar system in Fourier-BesovMorrey spaces. 1-31.

J. Sun, S. Cui (2015) Sharp well-posedness and ill-posedness in Fourier-Besov spaces for the viscous primitive equations of geophysics. arXiv:1510.0713v1

H. Triebel (1983) Theory of Function Spaces. 78.

E.J. Villamizar-Roa, M.A. Rodríguez-Bellido (2008) Global existence and exponential stability for the micropolar fluid system. 59(5), 790-809.

W. Zhu, J. Zhao (2018) Existence and regularizing rate estimates of solutions to the 3-D generalized micropolar system in Fourier-Besov spaces. 41(4), 1703-1722.

W. Zhu (2019) Sharp well-posedness and ill-posedness for the 3-D micropolar fluid system in Fourier-Besov spaces. 335-351.

Downloads

Published

2024-08-10

How to Cite

On the Well-Posedness for the 3-D Micropolar Fluid System in Critical Fourier-Besov-Morrey Spaces. (2024). London Journal of Research In Science: Natural and Formal, 24(10), 35-46. https://journalspress.uk/index.php/LJRS/article/view/1566