February 14, 2024Open Access

Classical solutions to a BGK-type model relaxing to the isentropic gas dynamics

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Abstract

In this paper, we consider a BGK-type kinetic model relaxing to the isentropic gas dynamics in the hydrodynamic limit. We introduce a linearization of the equation around the global equilibrium. Then we prove the global existence of classical solutions with an exponential convergence rate toward the equilibrium state in the periodic domain when the initial data is a small perturbation of the global equilibrium.

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Byung-Hoon Hwang (Wed,) studied this question.

synapsesocial.com/papers/68e79416b6db64358770571c https://doi.org/https://doi.org/10.48550/arxiv.2402.09653

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