Local well-posedness and blow up criterion for the Inviscid Boussinesq system in H\"{o}lder spaces

We prove the local in time existence and a blow up criterion of solution in the H\"{o}lder spaces for the inviscid Boussinesq system in $R^{N},N\geq2$, under the assumptions that the initial values $\theta_{0},u_{0}\in C^{r}$, with $r>1$.