浅水中浮式结构物：轴对称情况下的局部适定性适定性
Floating structures in shallow water: local well-posedness in the axisymmetric case
摘要：
浮式结构物问题描述了水面波浪和浮体（通常是船或波浪能转换器）之间的相互作用。如Lannes在[18]中所示，流体运动方程可以简化为一组关于表面高程和水平流量的两个发展方程。物体的存在是由物体下的排放约束来解释的;流体施加在这个物体上的压力就是与这个约束相关联的拉格朗日乘子。本文的目的是证明在浅水近似下，假设流动是轴对称的，没有漩涡的流固耦合问题的适定性。将流体方程写成拟线性双曲混合初边值问题，将固体方程写成与流体方程耦合的二阶常微分方程。最后，我们证明了这种耦合问题的局部时间适定性，提供了一些相容性条件的初始数据得到满足。
英文摘要：
The floating structure problem describes the interaction between surface water waves and a floating body, generally a boat or a wave energy converter. As shown by Lannes in [18] the equations for the fluid motion can be reduced to a set of two evolution equations on the surface elevation and the horizontal discharge. The presence of the object is accounted for by a constraint on the discharge under the object; the pressure exerted by the fluid on this object is then the Lagrange multiplier associated to this constraint. Our goal in this paper is to prove the well-posedness of this fluid-structure interaction problem in the shallow water approximation under the assumption that the flow is axisymmetric without swirl. We write the fluid equations as a quasilinear hyperbolic mixed initial boundary value problem and the solid equation as a second order ODE coupled to the fluid equations. Finally we prove the local in time well-posedness for this coupled problem, provided some compatibility conditions on the initial data are satisfied.
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