Keywords: non-Newtonian fluid; MHD equation; decay estimate; large initial perturbation
@article{10_21136_CMJ_2023_0230_21,
author = {Kim, Jae-Myoung},
title = {Upper and lower convergence rates for strong solutions of the {3D} {non-Newtonian} flows associated with {Maxwell} equations under large initial perturbation},
journal = {Czechoslovak Mathematical Journal},
pages = {395--413},
year = {2023},
volume = {73},
number = {2},
doi = {10.21136/CMJ.2023.0230-21},
mrnumber = {4586901},
zbl = {07729514},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0230-21/}
}
TY - JOUR AU - Kim, Jae-Myoung TI - Upper and lower convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under large initial perturbation JO - Czechoslovak Mathematical Journal PY - 2023 SP - 395 EP - 413 VL - 73 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0230-21/ DO - 10.21136/CMJ.2023.0230-21 LA - en ID - 10_21136_CMJ_2023_0230_21 ER -
%0 Journal Article %A Kim, Jae-Myoung %T Upper and lower convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under large initial perturbation %J Czechoslovak Mathematical Journal %D 2023 %P 395-413 %V 73 %N 2 %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0230-21/ %R 10.21136/CMJ.2023.0230-21 %G en %F 10_21136_CMJ_2023_0230_21
Kim, Jae-Myoung. Upper and lower convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under large initial perturbation. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 2, pp. 395-413. doi: 10.21136/CMJ.2023.0230-21
[1] Astarita, G., Marrucci, G.: Principles of Non-Newtonian Fluid Mechanics. McGraw-Hill, London (1974).
[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. | DOI | MR | JFM
[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. | MR | JFM
[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. | DOI | MR | JFM
[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. | DOI | MR | JFM
[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. | DOI | MR | JFM
[7] Karch, G., Pilarczyk, D.: Asymptotic stability of Landau solutions to Navier-Stokes system. Arch. Ration. Mech. Anal. 202 (2011), 115-131. | DOI | MR | JFM
[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. | DOI | MR | JFM
[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. | DOI | MR | JFM
[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. | DOI | MR | JFM
[11] Kozono, H.: Asymptotic stability of large solutions with large perturbation to the Navier-Stokes equations. J. Funct. Anal. 176 (2000), 153-197. | DOI | MR | JFM
[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. | DOI | MR | JFM
[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. | DOI | MR | JFM
[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. | DOI | MR | JFM
[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. | MR | JFM
[16] Schonbek, M. E.: Large time behaviour of solutions to the Navier-Stokes equations. Commun. Partial Differ. Equations 11 (1986), 733-763. | DOI | MR | JFM
[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. | DOI | MR | JFM
[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. | DOI | MR | JFM
[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). | MR | JFM
[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. | DOI | MR | JFM
[21] Zhou, Y.: Asymptotic stability for the 3D Navier-Stokes equations. Commun. Partial Differ. Equations 30 (2005), 323-333. | DOI | MR | JFM
[22] Zhou, Y.: Asymptotic stability for the Navier-Stokes equations in $L^n$. Z. Angew. Math. Phys. 60 (2009), 191-204. | DOI | MR | JFM
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