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We investigate the scalar resonances in the processes of $D^{0} \rightarrow\pi^{0}\pi^{0}\pi^{0}, \pi^{0}\pi^{0}\eta, \pi^{0}\eta\eta$ decays based on thechiral unitary approach for the final state interaction. We start from singlyCabibbo-suppressed production diagrams which provide a primary quark pair tohadronize two pseudoscalar mesons in $D^{0}$ decays. The resonances$f_{0}(500)$, $f_{0}(980)$ and $a_{0}(980)$ are dynamically produced from thefinal state interactions of the meson pairs. In our results, the experimentaldata for the $\pi^{0}\eta$ invariant mass spectrum of the $D^{0} \rightarrow\pi^{0}\eta\eta$ decay can be described well. We also make the predictions forthe $\pi^{0}\pi^{0}$ invariant mass spectrum of the $D^{0} \rightarrow\pi^{0}\pi^{0}\pi^{0}$, where the $f_{0}(980)$ can be found, and for the$\pi^{0}\pi^{0}$, $\pi^{0}\eta$ invariant mass spectrum of the $D^{0}\rightarrow \pi^{0}\pi^{0}\eta$, where the $f_{0}(500)$, $f_{0}(980)$ and$a_{0}(980)$ appear. Furthermore, the branching ratios of each decay channelare predicted. We expect more accurate measurements of these decays to betterunderstand the nature of the states $f_{0}(500)$, $f_{0}(980)$ and$a_{0}(980)$.

Scalar resonances in the final state interactions of the decays $D^{0} \rightarrow \pi^{0}\pi^{0}\pi^{0}, \pi^{0}\pi^{0}\eta,\pi^{0}\eta\eta$