We consider the global existence and asymptotic behavior of classical solutions for the polyatomic BGK model when the initial data starts sufficiently close to a global polyatomic Maxwellian. We observe that the linearized relaxation operator is decomposed into a polyatomic part and a monatomic-like part, leading to a dichotomy in the dissipative estimate in the sense that the degeneracy of the dissipation changes abruptly as the relaxation parameter $\theta$ reaches zero. Accordingly, we employ two different sets of micro-macro system to derive the full coercivity and close the energy estimate. 查看全文>>