  The disordered pyrochlore oxide Dy$_{2}$Zr$_{2}$O$_{7}$ shows the signatures
of field-induced spin freezing with remnant zero-point spin-ice entropy at 5
kOe magnetic field. We have performed zero-field and longitudinal field Muon
spin relaxation ($\mu$SR) studies on Dy$_{2}$Zr$_{2}$O$_{7}$. Our zero field
studies reveal the absence of both long-range ordering and spin freezing down
to 62 mK. The $\mu$SR relaxation rate exhibits a temperature-independent
plateau below 4 K, indicating a dynamic ground state of fluctuating spins
similar to the well-known spin ice system Dy$_{2}$Ti$_{2}$O$_{7}$. The
low-temperature spin fluctuations persist in the longitudinal field of 20 kOe
as well and show unusual field dependence of the relaxation rate, which is
uncommon for a spin-liquid system. Our results, combined with the previous
studies do not show any evidence of spin ice or spin glass ground state, rather
point to a disorder-induced dynamic magnetic ground state in the
Dy$_{2}$Zr$_{2}$O$_{7}$ material.
