  Granular gases demand models capable of capturing their distinct
characteristics. The widely employed inelastic hard-sphere model (IHSM)
introduces complexities that are compounded when incorporating realistic
features like surface roughness and rotational degrees of freedom, resulting in
the more intricate inelastic rough hard-sphere model (IRHSM). This paper
focuses on the inelastic rough Maxwell model (IRMM), presenting a more
tractable alternative to the IRHSM and enabling exact solutions. Building on
the foundation of the inelastic Maxwell model (IMM) applied to granular gases,
the IRMM extends the mathematical representation to encompass surface roughness
and rotational degrees of freedom. The primary objective is to provide exact
expressions for the Navier--Stokes--Fourier transport coefficients within the
IRMM, including the shear and bulk viscosities, the thermal and diffusive heat
conductivities, and the cooling-rate transport coefficient. In contrast to
earlier approximations in the IRHSM, our study unveils inherent couplings, such
as shear viscosity to spin viscosity and heat conductivities to counterparts
associated with a torque-vorticity vector. These exact findings provide
valuable insights into refining the Sonine approximation applied to the IRHSM,
contributing to a deeper understanding of the transport properties in granular
gases with realistic features.
