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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.13830 |
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| _version_ | 1866909082762346496 |
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| author | Chemetov, Nikolai V. Santos, Marcelo M. |
| author_facet | Chemetov, Nikolai V. Santos, Marcelo M. |
| contents | We analyze the Navier-Stokes equations for incompressible fluids with the {\lq\lq}viscous stress tensor{\rq\rq} $\mathbb{S}$ in a family which includes the Bingham model for viscoplastic fluids (more generally, the Herschel-Bulkley model). $\mathbb{S}$ is the subgradient of a convex potential $V=V(x,t,X)$, allowing that $V$ can depend on the space-time variables $(x,t)$. The potential has its one-sided directional derivatives $V'(X,X)$ uniformly bounded from below and above by a $p$-power function of the matrices $X$. For $p\geqslant 2.2$ we solve an initial boundary value problem for those fluid systems, in a bounded region in $\mathbb{R}^3$. We take a nonlinear boundary condition, which encompasses the Navier friction/slip boundary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13830 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A family of systems including the Herschel-Bulkley fluid equations Chemetov, Nikolai V. Santos, Marcelo M. Analysis of PDEs Mathematical Physics 35Q35, 74A20, 76S05 We analyze the Navier-Stokes equations for incompressible fluids with the {\lq\lq}viscous stress tensor{\rq\rq} $\mathbb{S}$ in a family which includes the Bingham model for viscoplastic fluids (more generally, the Herschel-Bulkley model). $\mathbb{S}$ is the subgradient of a convex potential $V=V(x,t,X)$, allowing that $V$ can depend on the space-time variables $(x,t)$. The potential has its one-sided directional derivatives $V'(X,X)$ uniformly bounded from below and above by a $p$-power function of the matrices $X$. For $p\geqslant 2.2$ we solve an initial boundary value problem for those fluid systems, in a bounded region in $\mathbb{R}^3$. We take a nonlinear boundary condition, which encompasses the Navier friction/slip boundary condition. |
| title | A family of systems including the Herschel-Bulkley fluid equations |
| topic | Analysis of PDEs Mathematical Physics 35Q35, 74A20, 76S05 |
| url | https://arxiv.org/abs/2401.13830 |