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In their study, Terrones et al. ["Rayleigh–Taylor instability at spherical interfaces between viscous fluids: The fluid/fluid interface," Phys. Fluids 32, 094105 (2020)] elucidated that investigations into the viscous Rayleigh–Taylor instability (RTI) in spherical geometry at a quiescent interface yield significant physical insights. Yet, the complexity amplifies when addressing a dynamic spherical interface pertinent to engineering and scientific inquiries. The dynamics of RTI, particularly when influenced by the Bell–Plesset effects at such interfaces, offers a rich tapestry for understanding perturbation growth. The evolution of this instability is describable by a coupled set of equations, allowing numerical resolution to trace the radius evolution and instability characteristics of a bubble akin to the implosion scenario of a fusion pellet in inertial confinement fusion scenarios. The investigation encompasses the impact of viscosity, external pressure, discrete mode, and a surface-tension-like force on the interfacial instability. In general, the oscillation of the bubble radius exhibits a decay rate that diminishes with increasing Reynolds number (Re). It is important to note that the growth of the perturbed amplitude is not only solely determined by the mechanical properties of the fluid but also by the dynamics of the interface. The low-order modal (n < 20) disturbance is dominant with relatively high Reynolds numbers. There is a specific mode corresponding the maximum in amplitude of perturbation in the linear phase, and the mode decreases as the Re decreases. The application of external pressure noticeably accelerates the bubble's oscillation and impedes its shrinkage, thereby preventing the bubble from collapsing completely. The increase in external pressure also promotes the transition from the first peak to the trough of the disturbance. At higher-order modes, the fluctuation of the disturbance curve tends to be uniform. The ultrahigh-order modes require a strong enough pressure to be excited. In addition, the smaller Weber number (We) helps to accelerate the bubble oscillation and promote the fluctuation of the disturbance amplitude, but has no significant effect on the time of the disturbance peak. These findings contribute to a deeper understanding of interfacial instabilities in the context of spherical bubbles and, especially, for the dynamics of fusion capsules in inertial confinement fusion. [ABSTRACT FROM AUTHOR]