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Abstract. 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.

Abstract. We introduce an optimal shaping problem based on Michell's wave resistance formula in order to find the form of a ship which has an immerged hull with minimal total resistance. The problem is to find a function u ∈ H 1 0 (D), even in the z-variable, and which minimizes the functionalwith an area constraint on the set {(x, z) ∈ D : u(x, z) = 0} and with the volume constraint D u(x, z)dxdz = V ; D is a bounded open subset of R 2 , symmetric about the x-axis, and k is Michell's kernel. We prove that u is locally α-Hölder continuous on D for all 0 < α < 2/5, and locally Lipschitz continuous onThe main assumption is the nonnegativity of u. We also prove that the area constraint is "saturated". The results are first derived for a general kernel k ∈ L q (D ×D) with q ∈ (1, +∞]. A numerical simulation illustrates the theoretical result.