Gubser flow is an axis-symmetric and boost-invariant evolution in a relativistic quantum field theory, providing a model for the evolution of matter produced in the wake of heavy-ion collisions. It is best studied by mapping $\mathbf{R}^{3,1}$ to $dS_{3}\times \mathbf{R}$ when the field theory has conformal symmetry. We show that at late de Sitter time, which corresponds to large proper time and central region in $\mathbf{R}^{3,1}$, the generic behavior for a holographic conformal field theory is given by $\varepsilon = P_T = - P_L$, with $\varepsilon$, $P_T$ and $P_L$ being the energy density, transverse and longitudinal pressures, respectively. We also establish the general late de Sitter time expansion, which when written in a suitable basis, systematically determines both the early proper time behavior and the behavior at large distance from the beam axis at any fixed proper time in the Minkowski frame. Particularly, $\varepsilon = P_T = - P_L$ is also generically realized at early proper time. The late de Sitter time expansion is also consistent with the hydrodynamic expansion at intermediate times.