A theoretical and numerical determination of optimal ship forms based on   Michell's wave resistance
  We determine the parametric hull of a given volume which minimizes the total water resistance for a given speed of the ship. The total resistance is the sum of Michell's wave resistance and of the viscous resistance, approximated by assuming a constant viscous drag coefficient. We prove that the optimized hull exists, is unique, symmetric, smooth and that it depends continuously on the speed. Numerical simulations show the efficiency of the approach, and complete the theoretical results. 
Julien Dambrine, Morgan Pierre, Germain Rousseaux
math.OC physics.flu-dyn