论文标题
三维的大型全球解决方案Navier-Stokes方程无垂直粘度
Large, global solutions to the three-dimensional the navier-stokes equations without vertical viscosity
论文作者
论文摘要
在一个方向上没有粘度的情况下，研究了三维，同质，不可压缩的Navier-Stokes方程。结果表明，有一个任意大的初始数据生成了独特的全局解决方案，其主要特征是它们逐渐在缺少粘度的方向上变化。困难是由于完全没有在这个方向上没有正则效应的原因。非线性项的特殊结构，即在速度场上具有无差异条件的关节，对于获得结果至关重要。
The three-dimensional, homogeneous, incompressible Navier-Stokes equations are studied in the absence of viscosity in one direction. It is shown that there are arbitrarily large initial data generating a unique global solution, the main feature of which is that they are slowly varying in the direction where viscosity is missing. The difficulty arises from the complete absence of a regularising effect in this direction. The special structure of the nonlinear term, joint with the divergence-free condition on the velocity field, is crucial in obtaining the result.
