一类时滞非牛顿流体在二维无界域上的适定性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (6): 1789-1802.

一类时滞非牛顿流体在二维无界域上的适定性

刘国威^*(),王启玲()

重庆师范大学数学科学学院重庆 401331

收稿日期:2022-11-07 修回日期:2023-03-02 出版日期:2023-12-26 发布日期:2023-11-16
通讯作者: *刘国威，E-mail: guoweiliu@cqnu.edu.cn
作者简介:王启玲，E-mail: 2690803827@qq.com
基金资助:
国家自然科学基金(12001073);重庆市自然科学基金(cstc2020jcyj-msxmX0709);重庆市教育委员会科学技术研究基金(KJQN201900563)

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

Liu Guowei^*(),Wang Qiling()

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331

Received:2022-11-07 Revised:2023-03-02 Online:2023-12-26 Published:2023-11-16
Supported by:
NSFC(12001073);NSF of Chongqing(cstc2020jcyj-msxmX0709);Science and Technology Research Foundation of Chongqing Education Commission(KJQN201900563)

摘要/Abstract

摘要：

该文研究了一类非自治的时滞不可压缩非牛顿流体在二维无界区域上的整体适定性. 在外力项具有最低正则性时, 该文结合空间区域分解技术和 Garlekin 方法建立了解的存在性, 然后利用能量估计的方法得到了解的唯一性和稳定性.

关键词: 非牛顿流体, 时滞, 适定性

Abstract:

In this paper, we study the well-poseness of a non-autonomous delayed incompressible non-Newtonian fluid on $2D$ unbounded domains. With a minimal regularity of the force, we prove the existence of solutions by the method of combining the technique of domain decomposition with the Garlerin approximation. Then we use the energy method to prove the uniqueness and the stability of solutions.

Key words: Non-Newtonian fluid, Delay, Well-posedness

中图分类号:

O373

刘国威, 王启玲. 一类时滞非牛顿流体在二维无界域上的适定性[J]. 数学物理学报, 2023, 43(6): 1789-1802.

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.

参考文献 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

Metrics

Viewed

Full text

182

HTML			PDF

Just accepted	Online first	Issue	Just accepted	Online first	Issue
0	0	0	0	0	182

	From	local

	Times	182
	Rate	100%

Abstract

Cited

Shared

Discussed