Local exact Lagrangian controllability for 1D barotropic compressible Navier--Stokes equations

Fuente: arXiv
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Main Authors: Koike, Kai, Sueur, Franck, Vergara-Hermosilla, Gastón
Format: Preprint
Published: 2024
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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