论文标题
最大$ l^1 $ regullity和不可压缩的Navier-Stokes方程在关键空间中
Maximal $L^1$-regularity and free boundary problems for the incompressible Navier-Stokes equations in critical spaces
论文作者
论文摘要
考虑到不可压缩的Navier-Stokes方程的时间依赖性的自由表面问题，这些方程描述了粘性不可压缩流体的运动几乎半空间。我们获得了问题的全局良好性，以在规模不变的临界空间中获得小的初始数据。我们的证明是基于最大$ l^1 $ - 在半空间和准线性术语的特殊结构中，来自坐标的拉格朗日变换出现的准线性术语的特殊结构。
Time-dependent free surface problem for the incompressible Navier-Stokes equations which describes the motion of viscous incompressible fluid nearly half-space are considered. We obtain global well-posedness of the problem for a small initial data in scale invariant critical Besov spaces. Our proof is based on maximal $L^1$-regularity of the corresponding Stokes problem in the half-space and special structures of the quasi-linear term appearing from the Lagrangian transform of the coordinate.
