Asymptotic analysis of a non-Newtonian fluid in a thin domain with Tresca law

Boukrouche, Mahdi; ELMIR, R

doi:10.1016/s0362-546x(04)00248-2

Cited by 20 publications

(21 citation statements)

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“…Using this estimate with Poincaré's inequality in the domain Ω, we obtain (19), for (20) to (24) according to (12), (13) , and (19). Because div (û ) = 0, by (13) and with a particular choice of the test function, we obtain (25) and (26). Finally, (27) follows from (14) to (16).…”

Section: Convergence Results and Limit Problem Corollary 41 Under Tmentioning

confidence: 97%

Study of generalized Stokes operator in a thin domain with friction law (casep< 2)

Dilmi

Benseridi

2018

Math Methods in App Sciences

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MSC Classification: 35R35; 76F10; 78M35 In this work, we consider a mathematical model of an incompressible fluid governed by the generalized Stokes system in a stationary regime in a 3-dimensional thin domain Ω with Tresca friction law. The problem statement and variational formulation of the problem are formulated. Then the estimates on velocity and pressure are proved in a fixed domain. Finally, our main goal concerns the specific Reynolds equation and the uniqueness of the solution (û ,̂) are obtained. KEYWORDS a priori estimates, Reynolds equation, Stokes systems, Tresca law, variational formulationHowever, in this case, the Stokes principle is not satisfied.These types of models were studied intensively in the 1980s and 1990s by Necas et al, 8 in which the authors studied the particular types of fluids, and describe the shear thickening (p > 2) and shear thinning (p < 2) phenomena. The author in other works 9,10 establish regularity results up to the boundary for solutions to generalized Stokes and Navier-Stokes systems of equations in the stationary and evolutive cases. The asymptotic analysis of the type (1), in a thin domain with Tresca and Coulomb friction has been studied in previous works. 11,12 In Boukrouche and EL Mir, 13 the authors proved the asymptotic analysis of a non-Newtonian and incompressible fluid with stress tensor (u , ) = |D(u )| −2 D(u ) − I, in a thin domain. In Bayada et al, 14 the authors consider the Navier-Stokes equations in a thin moving boundary domain.

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Section: Convergence Results and Limit Problem Corollary 41 Under Tmentioning

confidence: 97%

Study of generalized Stokes operator in a thin domain with friction law (casep< 2)

Dilmi

Benseridi

2018

Math Methods in App Sciences

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“…where, β > 0, Cμ > 0 and c > 0 are respectively deduced from, the embedding of V z in L 4 (Ω), the assumptionμ is Cμ-Lipschitz continuous function on R, and u * ,i ∈ B c . Therefore…”

Section: Study Of the Limit Problemmentioning

confidence: 99%

“…In Section 1, we recall the weak formulation of our coupled problem considered. Some estimates and convergence theorem by using the Korn and Poincaré inequalities (developed recently in Refs [3,4]) are given in Section 2. The limit problem with a specific weak form of the Reynolds equation, the uniqueness of the limit velocity and temperature are given in Section 3.…”

Section: Introductionmentioning

confidence: 99%

Study of the Non-isothermal Coupled Problem with Mixed Boundary Conditions in a Thin Domain with Friction Law

Saadallah¹,

Benseridi²,

Саадалах³

et al. 2018

J. Sib. Fed. Univ., Math. phys.

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This paper deals with the asymptotic behavior of a coupled system involving of an incompressible Bingham fluid and the equation of the heat energy, in a three-dimensional bounded domain with Tresca free boundary friction conditions. First we prove the existence and uniqueness results for the weak solution. Second, we show the strong convergence of the velocity and the temperature. Then a specific Reynolds limit equation is obtained, and the uniqueness of the limit velocity and temperature are proved.

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“…The literature concerning this topic is extensive (see e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). Further, let us mention the works which is realized by many authors in this area, for example, (see [2,4,9,10,[13][14][15][16][17][18][19][20][21]).…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Behavior of Solutions to Free Boundary Problem with Tresca Boundary Conditions

Saadallah

Chougui

Yazid

et al. 2021

Journal of Function Spaces

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In this paper, we study the asymptotic behavior of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. We study the limit when the ε tends to zero, we prove the convergence of the unknowns which are the velocity and the pressure of the fluid, and we obtain the limit problem and the specific Reynolds equation.

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Asymptotic analysis of a non-Newtonian fluid in a thin domain with Tresca law

Cited by 20 publications

References 0 publications

Study of generalized Stokes operator in a thin domain with friction law (casep< 2)

Study of generalized Stokes operator in a thin domain with friction law (casep< 2)

Study of the Non-isothermal Coupled Problem with Mixed Boundary Conditions in a Thin Domain with Friction Law

Asymptotic Behavior of Solutions to Free Boundary Problem with Tresca Boundary Conditions

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