Title: | Upper and lower convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under large initial perturbation (English) |
Author: | Kim, Jae-Myoung |
Language: | English |
Journal: | Czechoslovak Mathematical Journal |
ISSN: | 0011-4642 (print) |
ISSN: | 1572-9141 (online) |
Volume: | 73 |
Issue: | 2 |
Year: | 2023 |
Pages: | 395-413 |
Summary lang: | English |
. | |
Category: | math |
. | |
Summary: | We show the upper and lower bounds of convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under a large initial perturbation. (English) |
Keyword: | non-Newtonian fluid |
Keyword: | MHD equation |
Keyword: | decay estimate |
Keyword: | large initial perturbation |
MSC: | 35B35 |
MSC: | 35Q30 |
MSC: | 76A05 |
idZBL: | Zbl 07729514 |
idMR: | MR4586901 |
DOI: | 10.21136/CMJ.2023.0230-21 |
. | |
Date available: | 2023-05-04T17:43:49Z |
Last updated: | 2023-09-13 |
Stable URL: | http://hdl.handle.net/10338.dmlcz/151664 |
. | |
Reference: | [1] Astarita, G., Marrucci, G.: Principles of Non-Newtonian Fluid Mechanics.McGraw-Hill, London (1974). |
Reference: | [2] Bae, H.-O., Jin, B. J.: Upper and lower bounds of temporal and spatial decays for the Navier-Stokes equations.J. Differ. Equations 209 (2005), 365-391. Zbl 1062.35058, MR 2110209, 10.1016/j.jde.2004.09.011 |
Reference: | [3] Benvenutti, M. J., Ferreira, L. C. F.: Existence and stability of global large strong solutions for the Hall-MHD system.Differ. Integral Equ. 29 (2016), 977-1000. Zbl 1389.35255, MR 3513590 |
Reference: | [4] Gunzburger, M. D., Ladyzhenskaya, O. A., Peterson, J. S.: On the global unique solvability of initial-boundary value problems for the coupled modified Navier-Stokes and Maxwell equations.J. Math. Fluid Mech. 6 (2004), 462-482. Zbl 1064.76118, MR 2101892, 10.1007/s00021-004-0107-9 |
Reference: | [5] Guo, B., Zhu, P.: Algebraic $L^2$ decay for the solution to a class system of non-Newtonian fluid in $\mathbb R^n$.J. Math. Phys. 41 (2000), 349-356. Zbl 0989.35108, MR 1738602, 10.1063/1.533135 |
Reference: | [6] Kang, K., Kim, J.-M.: Existence of solutions for the magnetohydrodynamics with power- law type nonlinear viscous fluid.NoDEA, Nonlinear Differ. Equ. Appl. 26 (2019), Article ID 11, 24 pages. Zbl 1417.76045, MR 3924622, 10.1007/s00030-019-0557-7 |
Reference: | [7] Karch, G., Pilarczyk, D.: Asymptotic stability of Landau solutions to Navier-Stokes system.Arch. Ration. Mech. Anal. 202 (2011), 115-131. Zbl 1256.35061, MR 2835864, 10.1007/s00205-011-0409-z |
Reference: | [8] Karch, G., Pilarczyk, D., Schonbek, M. E.: $L^2$-asymptotic stability of singular solutions to the Navier-Stokes system of equations in $\mathbb{R}^3$.J. Math. Pures Appl. (9) 108 (2017), 14-40. Zbl 1368.35207, MR 3660767, 10.1016/j.matpur.2016.10.008 |
Reference: | [9] Kim, J.-M.: Temporal decay of strong solutions to the magnetohydrodynamics with power-law type nonlinear viscous fluid.J. Math. Phys. 61 (2020), Article ID 011504, 6 pages. Zbl 1432.76289, MR 4047930, 10.1063/1.5128708 |
Reference: | [10] Kim, J.-M.: Time decay rates for the coupled modified Navier-Stokes and Maxwell equations on a half space.AIMS Math. 6 (2021), 13423-13431. Zbl 07533493, MR 4332321, 10.3934/math.2021777 |
Reference: | [11] Kozono, H.: Asymptotic stability of large solutions with large perturbation to the Navier-Stokes equations.J. Funct. Anal. 176 (2000), 153-197. Zbl 0970.35106, MR 1784412, 10.1006/jfan.2000.3625 |
Reference: | [12] Miyakawa, T.: On upper and lower bounds of rates of decay for nonstationary Navier- Stokes flows in the whole space.Hiroshima Math. J. 32 (2002), 431-462. Zbl 1048.35063, MR 1954053, 10.32917/hmj/1151007491 |
Reference: | [13] Nečasová, Š., Penel, P.: $L^2$ decay for weak solution to equations of non-Newtonian incompressible fluids in the whole space.Nonlinear Anal., Theory Methods Appl., Ser. A 47 (2001), 4181-4191. Zbl 1042.76504, MR 1972358, 10.1016/S0362-546X(01)00535-1 |
Reference: | [14] Oliver, M., Titi, E. S.: Remark on the rate of decay of higher order derivatives for solutions to the Navier-Stokes equations in $\mathbb R^n$.J. Funct. Anal. 172 (2000), 1-18. Zbl 0960.35081, MR 1749867, 10.1006/jfan.1999.3550 |
Reference: | [15] Samokhin, V. N.: A magnetohydrodynamic-equation system for a nonlinearly viscous liquid.Differ. Equations 27 (1991), 628-636 translation from Differ. Uravn. 27 1991 886-896. Zbl 0795.76094, MR 1117118 |
Reference: | [16] Schonbek, M. E.: Large time behaviour of solutions to the Navier-Stokes equations.Commun. Partial Differ. Equations 11 (1986), 733-763. Zbl 0607.35071, MR 0837929, 10.1080/03605308608820443 |
Reference: | [17] Secchi, P.: $L^2$ stability for weak solutions of the Navier-Stokes equations in $\mathbb R^3$.Indiana Univ. Math. J. 36 (1987), 685-691. Zbl 0635.35076, MR 0905619, 10.1512/iumj.1987.36.36039 |
Reference: | [18] Wiegner, M.: Decay results for weak solutions of the Navier-Stokes equations on $\mathbb R^n$.J. Lond. Math. Soc., II. Ser. 35 (1987), 303-313. Zbl 0652.35095, MR 0881519, 10.1112/jlms/s2-35.2.303 |
Reference: | [19] Wilkinson, W. L.: Non-Newtonian Fluids: Fluid Mechanics, Mixing and Heat Transfer.International Series of Monographs on Chemical Engineering 1. Pergamon Press, New York (1960). Zbl 0124.41802, MR 0110392 |
Reference: | [20] Xie, Q., Guo, Y., Dong, B.-Q.: Upper and lower convergence rates for weak solutions of the 3D non-Newtonian flows.J. Math. Anal. Appl. 494 (2021), Article ID 124641, 21 pages. Zbl 1457.76027, MR 4161399, 10.1016/j.jmaa.2020.124641 |
Reference: | [21] Zhou, Y.: Asymptotic stability for the 3D Navier-Stokes equations.Commun. Partial Differ. Equations 30 (2005), 323-333. Zbl 1142.35548, MR 2131057, 10.1081/PDE-200037770 |
Reference: | [22] Zhou, Y.: Asymptotic stability for the Navier-Stokes equations in $L^n$.Z. Angew. Math. Phys. 60 (2009), 191-204. Zbl 1293.76049, MR 2486152, 10.1007/s00033-008-7045-y |
. |
Fulltext not available (moving wall 24 months)