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Abstract
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We study on the whole space
the compressible Euler system with damping coupled to the Poisson equation when
the damping coefficient tends towards infinity. We first prove a result of global
existence for the Euler–Poisson system in the case where the damping is large
enough, then, in a second step, we rigorously justify the passage to the limit to the
parabolic-elliptic Keller–Segel after performing a diffusive rescaling, and get an
explicit convergence rate. The overall study is carried out in “critical” Besov spaces,
in the spirit of the recent survey by R. Danchin devoted to partially dissipative
systems.
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Keywords
critical regularity, relaxation limit, partially
dissipative, Euler–Poisson equations, Keller–Segel
equations
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Mathematical Subject Classification
Primary: 35A01
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Milestones
Received: 18 July 2023
Revised: 24 January 2024
Accepted: 3 March 2024
Published: 30 September 2024
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