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Preprints, Working Papers, ... Year : 2017

REGULARITY OF OPTIMAL SHIP FORMS BASED ON MICHELL'S WAVE RESISTANCE

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 functional J(u) = D |u(x, z)| 2 dxdz + D D k(x, z, x , z)u(x, z)u(x , z)dxdzdx dz with 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 on D = {(x, z) ∈ D : z = 0}. The 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, +∞].
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Dates and versions

hal-01383229 , version 1 (18-10-2016)
hal-01383229 , version 2 (18-10-2017)

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Julien Dambrine, Morgan Pierre. REGULARITY OF OPTIMAL SHIP FORMS BASED ON MICHELL'S WAVE RESISTANCE. 2017. ⟨hal-01383229v2⟩
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