Evolution of Gravitationally Unstable de Sitter Compactifications

We study the time evolution of unstable $d{S}_p$ \times $S^q$ configurations with flux in theories of gravity with a cosmological constant. For certain values of the flux, we identify a stable configuration to which these unstable solutions flow. For other values of the flux the sphere wants to decompactify, regardless of the sign of the initial perturbation.