Extensive ab initio density functional theory molecular dynamics calculations were used to evaluate stability conditions for relevant phases of InN. In particular, the p-T conditions of the thermal decomposition of InN and pressure-induced wurtzite-rocksalt solid-solid phase transition were established. The comparison of the simulation results with the available experimental data allowed for a critical evaluation of the capabilities and limitations of the proposed simulation method. It is shown that ab initio molecular dynamics can be used as an efficient tool for simulations of phase transformations of InN, including solid-solid structural transition and thermal decomposition with formation of N2 molecules. It is of high interest, because InN is an important component of epitaxial quantum structures, but it has not been obtained as a bulk single crystal. This makes it difficult to determine its basic physical properties to develop new applications.