论文标题
粘度问题的水波的适合性
Well-posedness of the water-wave with viscosity problem
论文作者
论文摘要
在本文中，我们研究了具有粘度的表面重力波的运动。特别是我们证明了两个适当的结果。一方面，我们在Sobolev空间中建立了局部溶解度，以进行任意耗散。另一方面，我们在维纳（Wiener）空间中建立了全球良好的稳定性，具有足够大的粘度。这些结果是DIAS，Dyachenko \＆Zakharov System（{\ em Physics Letters A} 2008）的第一个严格证明，当未考虑表面张力时，将重力波建模为粘度。
In this paper we study the motion of a surface gravity wave with viscosity. In particular we prove two well-posedness results. On the one hand, we establish the local solvability in Sobolev spaces for arbitrary dissipation. On the other hand, we establish the global well-posedness in Wiener spaces for a sufficiently large viscosity. These results are the first rigorous proofs of well-posedness for the Dias, Dyachenko \& Zakharov system ({\em Physics Letters A} 2008) modelling gravity waves with viscosity when surface tension is not taken into account.
