Homogeneous incompressible Bingham viscoplastic as a limit of bi-viscosity fluids
In this paper, the existence of a weak solution for homogeneous incompressible Bingham fluid is investigated. The rheology of such a fluid is defined by a yield stress τ y and a discontinuous stress–strain law. This non-Newtonian fluid behaves like a solid at low stresses and like a non-linear fluid...
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| Veröffentlicht in: | Journal of elliptic and parabolic equations 2023-12, Vol.9 (2), p.705-724 |
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| container_title | Journal of elliptic and parabolic equations |
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| creator | Aberqi, Ahmed Aboussi, Wassim Benkhaldoun, Fayssal Bennouna, Jaouad Bradji, Abdallah |
| description | In this paper, the existence of a weak solution for homogeneous incompressible Bingham fluid is investigated. The rheology of such a fluid is defined by a yield stress
τ
y
and a discontinuous stress–strain law. This non-Newtonian fluid behaves like a solid at low stresses and like a non-linear fluid above the yield stress. In this work we propose to build a weak solution for Navier stokes Bingham equations using a bi-viscosity fluid as an approximation, in particular, we proved that the bi-viscosity tensor converges weakly to the Bingham tensor. This choice allowed us to show the existence of solutions for a given data
f
∈
L
2
(
0
,
T
;
V
′
)
. |
| doi_str_mv | 10.1007/s41808-023-00221-z |
| format | Article |
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τ
y
and a discontinuous stress–strain law. This non-Newtonian fluid behaves like a solid at low stresses and like a non-linear fluid above the yield stress. In this work we propose to build a weak solution for Navier stokes Bingham equations using a bi-viscosity fluid as an approximation, in particular, we proved that the bi-viscosity tensor converges weakly to the Bingham tensor. This choice allowed us to show the existence of solutions for a given data
f
∈
L
2
(
0
,
T
;
V
′
)
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τ
y
and a discontinuous stress–strain law. This non-Newtonian fluid behaves like a solid at low stresses and like a non-linear fluid above the yield stress. In this work we propose to build a weak solution for Navier stokes Bingham equations using a bi-viscosity fluid as an approximation, in particular, we proved that the bi-viscosity tensor converges weakly to the Bingham tensor. This choice allowed us to show the existence of solutions for a given data
f
∈
L
2
(
0
,
T
;
V
′
)
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τ
y
and a discontinuous stress–strain law. This non-Newtonian fluid behaves like a solid at low stresses and like a non-linear fluid above the yield stress. In this work we propose to build a weak solution for Navier stokes Bingham equations using a bi-viscosity fluid as an approximation, in particular, we proved that the bi-viscosity tensor converges weakly to the Bingham tensor. This choice allowed us to show the existence of solutions for a given data
f
∈
L
2
(
0
,
T
;
V
′
)
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s41808-023-00221-z</doi><tpages>20</tpages><orcidid>https://orcid.org/0000-0003-1186-5184</orcidid><orcidid>https://orcid.org/0000-0002-3156-3303</orcidid><orcidid>https://orcid.org/0000-0002-5889-492X</orcidid></addata></record> |
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| subjects | Mathematics Mathematics and Statistics Partial Differential Equations |
| title | Homogeneous incompressible Bingham viscoplastic as a limit of bi-viscosity fluids |
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