Control of homogeneous shear flow of multimode Maxwell fluids

Savel'ev, E. V.; Renardy, Michael

doi:10.1016/j.jnnfm.2009.10.006

Cited by 7 publications

(4 citation statements)

References 8 publications

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“…This is a genuine obstacle to deriving the controllability result for the nonlinear viscoelastic system from the result obtained for the linear system, because the stress for the nonlinear system is not the symmetric part of a gradient. Even the characterization of the set of reachable states seems to be a very difficult problem on which only fragmentary results are known [18][19][20]23].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Lack of null controllability of viscoelastic flows

2019

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Lack of null controllability of viscoelastic flows

2019

Self Cite

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“…In all these results for linear viscoelastic flows in higher dimensions, control of the stress tensor is possible only under the constraint that the stress is the symmetric part of a gradient. This is the main hindrance to work with nonlinear viscoelastic model and only few results are available [28,29,33] regarding the characterization of the set of reachable states.…”

Section: Introductionmentioning

confidence: 99%

Approximate controllability and stabilizability of a linearized system for the interaction between a viscoelastic fluid and a rigid body

Mitra

Roy

Takahashi

2021

Math. Control Signals Syst.

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We study control properties of a linearized fluid-structure interaction system, where the structure is a rigid body and where the fluid is a viscoelastic material. We establish the approximate controllability and the exponential stabilizability for the velocities of the fluid and of the rigid body and for the position of the rigid body. In order to prove this, we prove a general result for this kind of systems that generalizes in particular the case without structure. The exponential stabilization of the system is obtained with a finite-dimensional feedback control acting only on the momentum equation on a subset of the fluid domain and up to some rate that depends on the coefficients of the system. We also show that, as in the case without structure, the system is not exactly null-controllable in finite time.

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“…As an important class of non-Newtonian fluids, viscoelastic fluids show the properties of both elasticity and viscosity. Plenty of models have been proposed to describe the response characteristics of these fluids, among which the Maxwell model has been studied most widely [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Time-space dependent fractional viscoelastic MHD fluid flow and heat transfer over accelerating plate with slip boundary

Chen

Zheng

et al. 2017

THERM SCI

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The MHD flow and heat transfer of viscoelastic fluid over an accelerating plate with slip boundary are investigated. Different from most classical works, a modified time-space dependent fractional Maxwell fluid model is proposed in depicting the constitutive relationship of the fluid. Numerical solutions are obtained by explicit finite difference approximation and exact solutions are also presented for the limiting cases in integral and series forms. Furthermore, the effects of parameters on the flow and heat transfer behavior are analyzed and discussed in detail.

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Control of homogeneous shear flow of multimode Maxwell fluids

Cited by 7 publications

References 8 publications

Lack of null controllability of viscoelastic flows

Lack of null controllability of viscoelastic flows

Approximate controllability and stabilizability of a linearized system for the interaction between a viscoelastic fluid and a rigid body

Time-space dependent fractional viscoelastic MHD fluid flow and heat transfer over accelerating plate with slip boundary

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