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We suggest a time-dependent mean-field hydrodynamic model for a binarydipolar boson-fermion mixture to study the stability and collapse of fermionsin the $^{164}$Dy-$^{161}$Dy mixture. The condition of stability of the dipolarmixture is illustrated in terms of phase diagrams. A collapse is induced in adisk-shaped stable binary mixture by jumping the interspecies contactinteraction from repulsive to attractive by the Feshbach resonance technique.The subsequent dynamics is studied by solving the time-dependent mean-fieldmodel including three-body loss due to molecule formation in boson-fermion andboson-boson channels. Collapse and fragmentation in the fermions aftersubsequent explosions are illustrated. The anisotropic dipolar interactionleads to anisotropic fermionic density distribution during collapse. Thepresent study is carried out in three-dimensional space using realistic valuesof dipolar and contact interactions.

Stability and collapse of fermions in a binary dipolar boson-fermion 164Dy-161Dy mixture