Existence and regularity of pullback attractors for an incompressible non-Newtonian fluid with delays

Zhao, Caidi; Zhou, Sizhong; Li, Yongsheng

doi:10.1090/s0033-569x-09-01146-2

Cited by 13 publications

(3 citation statements)

References 58 publications

(98 reference statements)

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“…There are many works concerning the unique existence, regularity and long-term behavior of solutions to equations (2.11)-(2.14) or its associated versions (see e.g. [4,5,6,12,13,14,18,21,24,28,34,36,37,38,39,40,41,42]). …”

Section: Preliminariesmentioning

confidence: 99%

Dynamics of non-autonomous equations of non-Newtonian fluid on 2D unbounded domains

Zhao

2013

Dynamics of Partial Differential Equations

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Abstract. This paper studies the asymptotic behavior of solutions for a non-autonomous incompressible non-Newtonian fluid on two-dimensional unbounded domains. We first prove the existences of the L 2 -regularity uniformand H 2 -regularity uniform attractor A V, respectively. Then we establish the regularity of the uniform attractors by showingwhich implies the uniform (with respect to the external forces) asymptotic smoothing effect of the non-autonomous fluid in the sense that the solutions become eventually more regular than the initial data.

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Section: Preliminariesmentioning

confidence: 99%

Dynamics of non-autonomous equations of non-Newtonian fluid on 2D unbounded domains

Zhao

2013

Dynamics of Partial Differential Equations

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“…There are many papers on the existence and uniqueness, regularity and long‐term behavior of solutions to Equations or to its related versions. We can refer to and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Approximation of the incompressible non‐Newtonian fluid equations by the artificial compressibility method

Zhao

2012

Math Methods in App Sciences

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This paper studies the approximation of the non-Newtonian fluid equations by the artificial compressibility method. We first introduce a family of perturbed compressible non-Newtonian fluid equations (depending on a positive parameter ) that approximates the incompressible equations as ! 0 C . Then, we prove the unique existence and convergence of solutions for the compressible equations to the solutions of the incompressible equations.From the Stokes law (see, for example, [1], P 13 ), we see that if the dependence of u on e.u/ is linear, for example,then the Equations (1.1) and (1.2) are the well-known incompressible Navier-Stokes equations. The incompressibility of the fluid is described by div u D 0. An incompressible fluid, the behavior of which is characterized by the Stokes law (1.3), is called Newtonian fluid. Fluids that cannot be adequately described by (1.3) are usually called non-Newtonian fluids.The constitutive relations for an isothermal, nonlinear bipolar viscous two-dimensional (2D) fluid that were introduced in [1, 2] have the form ij .u/ D pı ij C 2 0 Á C je.u/j 2 Compared with the incompressible non-Newtonian fluid Equations (1.7) and (1.8), Equations (1.11) and (1.12) overcome the computational difficulties connected with the constraint 'div u D 0' . It is easier to approximate than the original incompressible equations as the constraint 'div u D 0' has been replaced by the evolution Equation (1.12).Obviously, the perturbed compressible non-Newtonian fluid Equations (1.11)-(1.14) turn to be the incompressible non-Newtonian fluid Equations (1.7)-(1.10) as D 0. Following this clue, the problems are now the following:Now, we can define a continuous functional B.u, v/ from V V to V 0 by hB.u, v/, vi D b.u, v, w/, 8 Especially, we set B.u/ D B.u, u/.

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“…Real [29,30] analyzed some new regularity results of pullback attractors for 2D Navier-Stokes equations with delays. In the case of incompressible non-Newtonian fluids with delays involving fourth-order operators, C. Zhao et al [62,66] investigated the existence of solutions and pullback attractors and L. Liu, T. Caraballo and X. Fu [43] analyzed their exponential stability.…”

Section: Nous Pouvons Réver D'équations Fonctionnelles Plus Compliqué...mentioning

confidence: 99%

Asymptotic analysis to non-autonomous systems of incompressible nonnewtonian fluids

Ledgar López Lázaro

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Agradeço à minha avó, María del Rosario, embora ela não esteja mais conosco, ela é a principal autora de todas as minhas realizações, Infinitas gracias mi viejita hermosa. Aos meus pais, Sra. Blanca Lázaro e Sr. Alfonso López, que com amor e, acima de tudo, confiança deixaram tomar minhas próprias decisões e me apoiaram até o fim, Infinitas gracias papitos lindos. À minha companheira de vida, luta, aventura, minha namorada Jackeline del Carmen, que faz parte deste trabalho, porque o viu nascer há 11 anos e tem estado em todas as etapas até hoje, Gracias mi amor. Para meus irmãos Lenard, Lenz e Levi, pelo apoio incondicional de estar sempre lá para, mim Gracias mis cholos vagos.Agradeço à Professora Dra. Gabriela Del Valle Planas, pela confiança, orientação, comprometimento e dedicação proporcionada no processo de doutorado, que fez que seja uma etapa muito agradável, abrindo inúmeraveis novas oportunidades neste maravilhoso mundo da pesquisa. Agradeço ao Professor Dr. Pedro Marin Rubio, pela amizade, oportunidade de trabalhar com ele e por ter aberto as portas da Universidad de Sevilla, tornando esta uma estância confortável.Um agradecimento especial aos meus grandes amigos, Lizeth Santa Cruz e John Matos, que fazem parte da minha família e da minha vida.Um agradecimento especial ao meu bom amigo e irmão da vida, Carlos Troncos Sanchez, pela ajuda e conselhos na redação deste trabalho.No final, mas não por último, para agradecer a confiança e o laço inabalável, meu bom amigo de aventura, bom irmão dos conselhos e compadre, porque a vida queria dessa maneira, Sr. Martin Salinas Albarran. Obrigado por tudo.O presente trabalho foi realizado com apoio da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES) -Código de Financiamento 001 e do Conselho Nacional de Desenvolvimento Científico e Tecnológico -CNPq, processo n o 2018/140649-2.Agradeço ao SANTANDER e IMUS pelo apoio financeiro para a realização do período co-tutela/sandwich na Universidad de Sevilla.

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Existence and regularity of pullback attractors for an incompressible non-Newtonian fluid with delays

Cited by 13 publications

References 58 publications

Dynamics of non-autonomous equations of non-Newtonian fluid on 2D unbounded domains

Dynamics of non-autonomous equations of non-Newtonian fluid on 2D unbounded domains

Approximation of the incompressible non‐Newtonian fluid equations by the artificial compressibility method

Asymptotic analysis to non-autonomous systems of incompressible nonnewtonian fluids

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