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Non-local hydrodynamics as a slow manifold for the one-dimensional kinetic equation

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We prove an explicit, non-local hydrodynamic closure for the linear one-dimensional kinetic equation independent on the size of the relaxation time. We compare this dynamical equation to the local approximations… Click to show full abstract

We prove an explicit, non-local hydrodynamic closure for the linear one-dimensional kinetic equation independent on the size of the relaxation time. We compare this dynamical equation to the local approximations obtained from the Chapmanā€“Enskog expansion for small relaxation times. Our results rely on the spectral theory of Jacobi operators with rank-one perturbations.

Keywords: dimensional kinetic; hydrodynamics; kinetic equation; equation; one dimensional; non local

Journal Title: Continuum Mechanics and Thermodynamics
Year Published: 2020

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