Exponential stability of an incompressible non-Newtonian fluid with delay

Linfang Liu; Toms Caraballo; Xianlong Fu

doi:10.3934/dcdsb.2018138

Exponential stability of an incompressible non-Newtonian fluid with delay

Linfang Liu, Toms Caraballo^*, Xianlong Fu

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The existence and uniqueness of stationary solutions to an incompressible non-Newtonian fluid are first established. The exponential stability of steady-state solutions is then analyzed by means of four di erent approaches. The first is the classical Lyapunov function method, while the second one is based on a Razumikhin type argument. Then, a method relying on the construction of Lyapunov functionals and another one using a Gronwall-like lemma are also exploited to study the stability, respectively. Some comments concerning several open research directions about this model are also included.

Original language	English
Pages (from-to)	4285-4303
Number of pages	19
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	23
Issue number	10
DOIs	https://doi.org/10.3934/dcdsb.2018138
State	Published - Dec 2018

Keywords

Delay
Exponential stability
Non-Newtonian fluids
Stationary solution

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10.3934/dcdsb.2018138

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abstract = "The existence and uniqueness of stationary solutions to an incompressible non-Newtonian fluid are first established. The exponential stability of steady-state solutions is then analyzed by means of four di erent approaches. The first is the classical Lyapunov function method, while the second one is based on a Razumikhin type argument. Then, a method relying on the construction of Lyapunov functionals and another one using a Gronwall-like lemma are also exploited to study the stability, respectively. Some comments concerning several open research directions about this model are also included.",

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author = "Linfang Liu and Toms Caraballo and Xianlong Fu",

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AU - Liu, Linfang

AU - Caraballo, Toms

AU - Fu, Xianlong

PY - 2018/12

Y1 - 2018/12

N2 - The existence and uniqueness of stationary solutions to an incompressible non-Newtonian fluid are first established. The exponential stability of steady-state solutions is then analyzed by means of four di erent approaches. The first is the classical Lyapunov function method, while the second one is based on a Razumikhin type argument. Then, a method relying on the construction of Lyapunov functionals and another one using a Gronwall-like lemma are also exploited to study the stability, respectively. Some comments concerning several open research directions about this model are also included.

AB - The existence and uniqueness of stationary solutions to an incompressible non-Newtonian fluid are first established. The exponential stability of steady-state solutions is then analyzed by means of four di erent approaches. The first is the classical Lyapunov function method, while the second one is based on a Razumikhin type argument. Then, a method relying on the construction of Lyapunov functionals and another one using a Gronwall-like lemma are also exploited to study the stability, respectively. Some comments concerning several open research directions about this model are also included.

KW - Delay

KW - Exponential stability

KW - Non-Newtonian fluids

KW - Stationary solution

UR - https://www.scopus.com/pages/publications/85054187731

U2 - 10.3934/dcdsb.2018138

DO - 10.3934/dcdsb.2018138

M3 - 文章

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JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 10

ER -

Exponential stability of an incompressible non-Newtonian fluid with delay

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