Breakup and encapsulation phenomena are analytically investigated for a gas-cored compound liquid jet which consists of an inviscid and incompressible core gas and surrounding annular liquid. Applying the long wave approximation to both core and annular phases, a set of reduced nonlinear equations is derived for large deformations of the jet. Breakup of the jet is numerically examined in the reduced equations when the jet is semi-infinite and sinusoidal disturbances are fed at the end of the jet. It is found that there exit the most unstable frequencies of disturbances giving the shortest breakup time, which increase as the increase of input amplitudes and velocity ratios of the core to the annular phases, while increase or decrease depending upon the Weber numbers based on the annular phase. For small and medium Weber numbers, it is shown that the jet breaks up by pinching of the core phase and the capsule formation periods and sizes can be determined by the most unstable frequencies, which well agree with the results in the previous experiment and the existing phenomenological model. On the other hand, it is also shown for large Weber numbers that the jet breaks up by disintegration of the annular phase and fails to encapsulate the core gas.

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