一类时滞非牛顿流体在二维无界域上的适定性

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O373

Liu Guowei, Wang Qiling. The Well-posedness of a Delayed Non-Newtonian Fluid on ${2D}$ Unbounded Domains[J].Acta mathematica scientia,Series A, 2023, 43(6): 1789-1802.

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References 26

[1]	Bellout H, Bloom F. Bounds for the dimensions of the attractors of nonlinear bipolar viscous fluids. Asymptotic Anal, 1995, 11: 131-167
[2]	Bellout H, Bloom F, Nečas J. Young measure-valued solutions for non-Newtonian incompressible viscous fluids. Comm PDE, 1994, 19: 1763-1803 doi: 10.1080/03605309408821073
[3]	Bellout H, Bloom F, Nečas J. Phenomenological behavior of multipolar viscous fluids. Quart Appl Math, 1992, 5: 559-583
[4]	Bellout H, Bloom F, Nečas J. Existence, uniqueness and stability of solutions to the initial boundary value problem for bipolar viscous fluids. Differential Integral Equations, 1995, 8: 453-464
[5]	Bloom F, Hao W. Regularization of a non-Newtonian system in an unbounded channel: Existence and uniqueness of solutions. Nonlinear Anal: TMA, 2001, 44: 281-309 doi: 10.1016/S0362-546X(99)00264-3
[6]	Bloom F, Hao W. Regularization of a non-Newtonian system in an unbounded channel: Existence of a maximal compact attractor. Nonlinear Anal: TMA, 2001, 43: 743-766 doi: 10.1016/S0362-546X(99)00232-1
[7]	Caraballo T, Real J. Navier-Stokes equations with delays. R Soc London Proc Ser A Math Phys Eng Sci, 2001, 457: 2441-2453
[8]	Garrido-Atienza M J, Marín-Rubio P. Navier Stokes equations with delays on unbounded domains. Nonlinear Anal: TMA, 2006, 64: 1100-1118 doi: 10.1016/j.na.2005.05.057
[9]	Jeong J, Park J. Pullback attractors for a $2D$-non-autonomous incompressible non-Newtonian fluid with variable delays. Discrete Contin Dyn Syst B, 2016, 21: 2687-2702 doi: 10.3934/dcdsb
[10]	Li Y, Zhao C. Global attractor for a system of the non-Newtonian incompressible fluid in 2D unbounded domains. Acta Anal Funct Appl, 2002, 4: 1009-1327
[11]	Lion P L. Quelques Méthodes De Résolution Des Problems Aux Limits Non Linéaires. Paris: Dunod, 1969
[12]	Liu G. Pullback asymptotic behavior of solutions for a 2D non-autonomous non-Newtonian fluid. J Math Fluid Mech, 2017, 19: 623-643 doi: 10.1007/s00021-016-0299-9
[13]	Liu L, Caraballo T, Fu X. Dynamics of a non-automous incompressible non-Newtonian fluid with dely. Dyn Partial Differ Equ, 2017, 14: 375-402 doi: 10.4310/DPDE.2017.v14.n4.a4
[14]	Liu L, Caraballo T, Fu X. Exponential stability of an incompressible non-Newtonian fluid with delay. Discrete Contin Dyn Syst B, 2018, 23: 4285-4303
[15]	Málek J, Nečas J, Rokyta M, Ružička M. Weak and Measure-Valued Solutions to Evolutionary PDE. New York: Champman-Hall, 1996
[16]	Nečas J, Silhavy M. Multipular viscous fluids. Quart Appl Math, 1991, XLIX(2): 247-265
[17]	Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. Berlin: Springer, 1997
[18]	Zhao C. Pullback asymptotic behavior of solutions for a non-autonomous non-Newtonian fluid on 2D unbounded domains. J Math Phys, 2012, 53: 1-22
[19]	Zhao C, Li Y. $H^2$-compact attractor for a non-Newtonian system in two-dimensional unbound domains. Nonlinear Anal, 2004, 56: 1091-1103 doi: 10.1016/j.na.2003.11.006
[20]	Zhao C, Li Y, Zhou S. Regularity of trajectory attractor and upper semicontinuity of global attractor for a 2D non-Newtonian fluid. J Differential Equations, 2009, 247: 2331-2363 doi: 10.1016/j.jde.2009.07.031
[21]	Zhao C, Liu G, An R. Global well-posedness and pullback attractors for an incompressible non-Newtonian fluid with infinite delays. Differ Equ Dyn Syst, 2017, 25: 39-64 doi: 10.1007/s12591-014-0231-9
[22]	Zhao C, Liu G, Wang W. Smooth pullback attractors for a non-autonomous 2D non-Newtonian fluid and their tempered behaviors. J Math Fluid Mech, 2014, 16: 243-262 doi: 10.1007/s00021-013-0153-2
[23]	赵才地, 阳玲, 刘国威, 许正雄. 类时滞非牛顿流方程组在二维无界区域上的整体适定性与拉回吸引子. 应用数学学报, 2017, 40(2): 287-311 doi: 10.12387/C2017025
	Zhao C, Yang L, Liu G, Hsu C. Global well-posenness and pullback attractor for a delayed non-Newtonian fluid on two dimensional unbounded domains. Acta Math Appl Sinica Chinese Ser, 2017, 40(2): 287-311 doi: 10.12387/C2017025
[24]	Zhao C, Zhou S. Uniform attractors for a nonautonomous incompressible non-Newtonian fluid with locally uniformly integrable external forces in distribution space. J Math Phys, 2007, 48: 032702 doi: 10.1063/1.2709845
[25]	Zhao C, Zhou S. Pullback attractors for a non-autonomous incompressible non-Newtonian fluid. J Differential Equations, 2007, 238: 394-425 doi: 10.1016/j.jde.2007.04.001
[26]	Zhao C, Zhou S, Li Y. Existence and regularity of pullback attractors for an incompressible non-Newtonian fluid with delays. Quart Appl Math, 2009, 67: 503-540 doi: 10.1090/qam/2009-67-03

The Well-posedness of a Delayed Non-Newtonian Fluid on ${2D}$ Unbounded Domains

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