We consider the global existence and asymptotic behavior of classical solutions to the ellipsoidal BGK model for polyatomic molecules when the initial data starts sufficiently close to a global polyatomic Maxwellian. We observe that the linearized relaxation operator is decomposed into a trully polyatomic part and a essentially monatomic part, leading to a dichotomy in the dissipative property in the sense that the degeneracy of the dissipation shows an abrupt jump 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.
Categories: math.AP