Stimulated by the newly discovered $Omega(2012)$ resonance at Belle II, in this work we have studied the OZI allowed strong decays of the low-lying $1P$- and $1D$-wave $Omega$ baryons within the $^3P_0$ model. It is found that $Omega(2012)$ is most likely to be a $1P$-wave $Omega$ state with $J^P=3/2^-$. We also find that the $Omega(2250)$ state could be assigned as a $1D$-wave state with $J^P=5/2^+$. The other missing $1P$- and $1D$-wave $Omega$ baryons may have large potentials to be observed in their main decay channels.
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