Problem Statement for the Rotation Profile of Galaxies

• The flat velocity profile problem.
  
  After attaining a maximal speed consistent with Newton's law of gravity near the core, the velocity profile stays flat with increasing distance. Newton's law predicts a "Keplerian" decline for the velocity of the outer stars.


• The stability problem.
  
  Thin spiral galaxies are mathematically unstable to small disturbances along the axis which should lead to collapse.