×

zbMATH — the first resource for mathematics

Global existence and exponential decay of strong solutions of nonhomogeneous magneto-micropolar fluid equations with large initial data and vacuum. (English) Zbl 1440.35283
Summary: The present paper concerns an initial boundary value problem of two-dimensional nonhomogeneous magneto-micropolar fluid equations with nonnegative density. We establish the global existence and exponential decay rates of strong solutions. In particular, the initial data can be arbitrarily large. The key idea is to use a lemma of B. Desjardins [Arch. Ration. Mech. Anal. 137, No. 2, 135–158 (1997; Zbl 0880.76090)].
MSC:
35Q35 PDEs in connection with fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76W05 Magnetohydrodynamics and electrohydrodynamics
35D35 Strong solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ahmadi, G.; Shahinpoor, M., Universal stability of magneto-micropolar fluid motions, Internat. J. Eng. Sci., 12, 657-663 (1974) · Zbl 0284.76009
[2] Amrouche, C.; Girault, V., Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czechoslovak Math. J., 44, 109-140 (1994) · Zbl 0823.35140
[3] Berkovski, B.; Bashtovoy, V., Magnetic Fluids and Applications Handbook (1996), New York: Begell House, New York
[4] Braz e. Silva, P.; Friz, L.; Rojas-Medar, MA, Exponential stability for magneto-micropolar fluids, Nonlinear Anal., 143, 211-223 (2016) · Zbl 1382.35208
[5] Cheng, J.; Liu, Y., Global regularity of the 2D magnetic micropolar fluid flows with mixed partial viscosity, Comput. Math. Appl., 70, 66-72 (2015)
[6] Choe, HJ; Kim, H., Strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids, Comm. Partial Differ. Equ., 28, 1183-1201 (2003) · Zbl 1024.76010
[7] Desjardins, B., Regularity results for two-dimensional flows of multiphase viscous fluids, Arch. Rational Mech. Anal., 137, 135-158 (1997) · Zbl 0880.76090
[8] Friedman, A., Partial Differential Equations (2008), New York: Dover Books on Mathematics, New York
[9] Gala, S., Regularity criteria for the 3D magneto-micropolar fluid equations in the Morrey-Campanato space, Nonlinear Differ. Equ. Appl., 17, 181-194 (2010) · Zbl 1191.35214
[10] Gilbarg, D.; Trudinger, NS, Elliptic Partial Differential Equations of Second Order (2001), Berlin: Springer, Berlin
[11] Li, M.; Shang, H., Large time decay of solutions for the 3D magneto-micropolar equations, Nonlinear Anal. Real World Appl., 44, 479-496 (2018) · Zbl 1404.35050
[12] Lions, PL, Mathematical Topics in Fluid Mechanics, vol. I: Incompressible Models (1996), Oxford: Oxford University Press, Oxford
[13] Lukaszewicz, G., Micropolar Fluids Theory and Applications (1999), Baston: Birkhäuser, Baston · Zbl 0923.76003
[14] Ma, L., On two-dimensional incompressible magneto-micropolar system with mixed partial viscosity, Nonlinear Anal. Real World Appl., 40, 95-129 (2018) · Zbl 1382.35231
[15] Rojas-Medar, MA, Magneto-micropolar fluid motion: existence and uniqueness of strong solution, Math. Nachr., 188, 301-319 (1997) · Zbl 0893.76006
[16] Shang, H.; Gu, C., Global regularity and decay estimates for 2D magneto-micropolar equations with partial dissipation, Z. Angew. Math. Phys., 70, 22 (2019) · Zbl 1417.35141
[17] Shang, H.; Zhao, J., Global regularity for 2D magneto-micropolar equations with only micro-rotational velocity dissipation and magnetic diffusion, Nonlinear Anal., 150, 194-209 (2017) · Zbl 1356.35187
[18] Song, S., On local strong solutions to the three-dimensional nonhomogeneous incompressible magnetohydrodynamic equations with density-dependent viscosity and vacuum, Z. Angew. Math. Phys., 69, 27 (2018) · Zbl 1392.35238
[19] Struwe, M., Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems (2008), Berlin: Springer, Berlin · Zbl 1284.49004
[20] Tan, Z.; Wu, W.; Zhou, J., Global existence and decay estimate of solutions to magneto-micropolar fluid equations, J. Differ. Equ., 266, 4137-4169 (2019) · Zbl 1457.76202
[21] Yuan, J., Existence theorem and blow-up criterion of the strong solutions to the magneto-micropolar fluid equations, Math. Methods Appl. Sci., 31, 1113-1130 (2008) · Zbl 1137.76071
[22] Zhang, P.; Zhu, M., Global regularity of 3D nonhomogeneous incompressible magneto-micropolar system with the density-dependent viscosity, Comput. Math. Appl., 76, 2304-2314 (2018)
[23] Zhong, X.: Local strong solutions to the Cauchy problem of two-dimensional nonhomogeneous magneto-micropolar fluid equations with nonnegative density. Anal. Appl. (Singap.). 10.1142/S0219530519500167
[24] Zhong, X.: Global strong solution to the 2D Cauchy problem of nonhomogeneous magneto-micropolar fluid equations with large initial data and vacuum, submitted for publication
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.