Local exact Lagrangian controllability for 1D barotropic compressible Navier--Stokes equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908443636400128 |
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| author | Koike, Kai Sueur, Franck Vergara-Hermosilla, Gastón |
| author_facet | Koike, Kai Sueur, Franck Vergara-Hermosilla, Gastón |
| contents | We consider a viscous compressible barotropic flow in the interval $[0,π]$ with homogeneous Dirichlet boundary conditions for the flow velocity and a constant rest state as initial data. Given two sufficiently close subintervals $I=[α_1,α_2]$ and $J=[β_1,β_2]$ of $(0,1)$, a nonempty open set $ω\subset (1,π)$, and $T>0$, we construct an external force $f$ supported in $ω$ acting on the momentum equation such that the corresponding flow map moves the fluid particles initially occupying $I$ exactly onto $J$ in time $T$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local exact Lagrangian controllability for 1D barotropic compressible Navier--Stokes equations Koike, Kai Sueur, Franck Vergara-Hermosilla, Gastón Analysis of PDEs We consider a viscous compressible barotropic flow in the interval $[0,π]$ with homogeneous Dirichlet boundary conditions for the flow velocity and a constant rest state as initial data. Given two sufficiently close subintervals $I=[α_1,α_2]$ and $J=[β_1,β_2]$ of $(0,1)$, a nonempty open set $ω\subset (1,π)$, and $T>0$, we construct an external force $f$ supported in $ω$ acting on the momentum equation such that the corresponding flow map moves the fluid particles initially occupying $I$ exactly onto $J$ in time $T$. |
| title | Local exact Lagrangian controllability for 1D barotropic compressible Navier--Stokes equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.19210 |