Global existence for the 3-D generalized micropolar fluid system in critical Fourier-Besov spaces with variable exponent. (English) Zbl 07814855
Summary: In this work, we study the 3-D generalized Cauchy problem of the incompressible micropolar fluid system (GMFS) in the critical variable exponent FourierBesov space \(\mathcal{F}\dot{\mathcal{B}}^{4-\frac{3}{p(\cdot)}-2\alpha}_{p(\cdot),q}\). We establish the global well-posedness result with the initial data belonging to \(\mathcal{F}\dot{\mathcal{B}}^{4-\frac{3}{p(\cdot)}-2\alpha}_{p(\cdot),q}\), where \(p=p (\cdot)\) is a bounded function satisfy \(p\in [2,\frac{6}{5-4\alpha}]\), \(\alpha \in (\frac{1}{2},1]\) and \(q\in [1, \frac{3}{2\alpha-1}]\).
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 70K20 | Stability for nonlinear problems in mechanics |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
References:
| [1] | Shaolei Ru and M. Z. Abidin. Global well-posedness of the incompressible fractional Navier-Stokes equations in Fourier-Besov spaces with variable exponent. Computers and Mathe-matics with Applications 77 (4) (2019) 1082-1090. · Zbl 1442.35354 |
| [2] | A. Almeida and P. Hästö. Besov spaces with variable smoothness and integrability. J. Funct. Anal. 258 (5) (2010) 1628-1655. · Zbl 1194.46045 |
| [3] | M. F. de Almeida, L. C. Ferreira and L. S. M. Lima. Uniform global well-posedness of the NavierStokes-Coriolis system in a new critical space. Math. Z. 287 (3-4) (2017) 735-750. · Zbl 1379.35220 |
| [4] | A. Azanzal, A. Abbassi, and C. Allalou. Existence of solutions for the Debye-Hückel system with low regularity initial data in critical Fourier-Besov-Morrey spaces. Nonlinear Dynamics and Systems Theory 21 (4) (2021) 367-380. · Zbl 1524.35295 |
| [5] | Q. Chen, and C. Miao. Global well-posedness for the micropolar fluid system in critical Besov spaces. J. Differential Equations 252 (3) (2012) 2698-2724. · Zbl 1234.35193 |
| [6] | M. Cannone, and G. Karch. Smooth or singular solutions to the Navier-Stokes system. J. Differential Equations 197 (2004) 247-274. · Zbl 1042.35043 |
| [7] | L. Diening, P. Harjulehto, P. Hästö and M. Råžicka. Lebesgue and Sobolev spaces with variable exponent. In: Lecture Notes in Mathematics, 2017. Springer, Heidelberg, 2011. · Zbl 1222.46002 |
| [8] | L. C. Ferreira and E. J. Villamizar-Roa. Micropolar fluid system in a space of distributions and large time behavior. J. Math. Anal. Appl. 332 (2) (2007) 1425-1445. · Zbl 1122.35109 |
| [9] | A. C. Eringen. Theory of micropolar fluids. J. Math. Mech. 16 (1966) 1-18. |
| [10] | G. P. Galdi and S. Rionero. A note on the existence and uniqueness of solutions of the micropolar fuid equations. International Journal of Engineering Science 15 (1977) 105-108. · Zbl 0351.76006 |
| [11] | J. Sun and S. Cui. Sharp well-posedness and ill-posedness in Fourier-Besov spaces for the viscous primitive equations of geophyscs. arXiv:1510.0713v1. (2015). |
| [12] | W. Zhu, and J. Zhao. Existence and regularizing rate estimates of solutions to the 3-D generalized micropolar system in Fourier-Besov spaces. Math. Methods Appl. Sci. 41 (4) (2018) 1703-1722. · Zbl 1393.35190 |
| [13] | W. Zhu. Sharp well-posedness and ill-posedness for the 3-D micropolar fluid system in Fourier-Besov spaces. Nonlinear Analysis: Real World Applications 46 (2019) 335-351. · Zbl 1412.35277 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
