Evolution of Gravitationally Unstable de Sitter Compactifications
  We study the time evolution of unstable $dS_p$ \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. 
C. Krishnan, S. Paban and M. Zanic