Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On unique solvability and regularity in the linearized two-dimensional wave resistance problem


Author: Dario Pierotti
Journal: Quart. Appl. Math. 61 (2003), 639-655
MSC: Primary 35J25; Secondary 35B65, 76B15
DOI: https://doi.org/10.1090/qam/2019616
MathSciNet review: MR2019616
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Abstract: We discuss existence, uniqueness, and regularity of the solutions of a boundary value problem in a strip, which is obtained by linearization of the equations of the wave-resistance problem for a cylinder semisubmerged in a heavy fluid of constant depth $ H$ and moving at uniform velocity $ c$ in the direction orthogonal to its generators. We show that the problem has a unique solution, rapidly decreasing at infinity, for every $ c > \sqrt {gH} $, where $ g$ is the acceleration of gravity. For $ c < \sqrt {gH} $, we prove unique solvability provided $ c \ne {c_k}$, where $ {c_k}$ is a known sequence monotonically decreasing to zero. In this case, the related flow has in general nontrivial oscillations at infinity downstream.


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DOI: https://doi.org/10.1090/qam/2019616
Article copyright: © Copyright 2003 American Mathematical Society


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