论文标题
粘性水波模型的全球适应性和衰减
Global well-posedness and decay for viscous water wave models
论文作者
论文摘要
不可压缩流体的自由表面的运动是一个非常活跃的研究区域。这些作品中的大多数研究了无粘性液体的情况。但是，在几种实际应用中，需要考虑粘性阻尼的情况。在本文中，我们得出了一种新的渐近模型，用于单向粘性水波的运动。特别是，我们在Sobolev空间中建立了全球良好的体现。此外，我们还建立了第四阶PDE建模双向水波的全局良好性和衰减，粘度在深水中移动，有或没有表面张力效应。
The motion of the free surface of an incompressible fluid is a very active research area. Most of these works examine the case of an inviscid fluid. However, in several practical applications, there are instances where the viscous damping needs to be considered. In this paper we derive and study a new asymptotic model for the motion of unidirectional viscous water waves. In particular, we establish the global well-posedness in Sobolev spaces. Furthermore, we also establish the global well-posedness and decay of a fourth order PDE modelling bidirectional water waves with viscosity moving in deep water with or without surface tension effects.
