论文标题
非线性六阶薄膜方程作为流体 - 结构相互作用问题的降低模型的理由
Justification of a nonlinear sixth-order thin-film equation as the reduced model for a fluid -- structure interaction problem
论文作者
论文摘要
从粘性流体的薄层和薄弹性结构之间的非线性2D/1D流体结构相互作用问题开始，在相对流体厚度的消失极限上，我们严格地得出了六阶薄膜方程，描述了结构的垂直位移的动力学。该过程基本上是基于定量能量估计值，根据相对流体厚度进行量化，以及结构和固体底物之间的均匀无接触率。六阶薄膜方程是有理由将重新定位与薄膜方程的独特阳性经典解的强烈收敛意义的。此外，极限流体速度和压力可以仅以薄膜方程的解决方案表示。
Starting from a nonlinear 2D/1D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic structure, on the vanishing limit of the relative fluid thickness, we rigorously derive a sixth-order thin-film equation describing the dynamics of vertical displacements of the structure. The procedure is essentially based on quantitative energy estimates, quantified in terms of the relative fluid thickness, and a uniform no-contact result between the structure and the solid substrate. The sixth-order thin-film equation is justified in the sense of strong convergence of rescaled structure displacements to the unique positive classical solution of the thin-film equation. Moreover, the limit fluid velocity and the pressure can be expressed solely in terms of the solution to the thin-film equation.
