论文标题
在加权Hölder空间上的De Rham复合物的Fredholm Navier-Stokes类型方程
The Fredholm Navier-Stokes type equations for the de Rham complex over weighted Hölder spaces
论文作者
论文摘要
我们考虑了De Rham复合物在$ {\ Mathbb r}^n \ times [0，t] $，$ n \ geq 2 $中生成的Navier-Stokes类型方程的初始问题家族，其在刻度上具有正时$ t $，比例$ t $加权了AnisotropicHölderSpace。随着权重控制无穷大的零级相对于考虑载体场的空间变量，这实际上会导致在无限段的单数圆锥点上紧凑的歧管上的初始问题。我们证明，家庭中的每个问题都会引起弗雷德尔姆开放的注射映射，以衡量量表的元素。在该综合体的步骤$ 1 $上，我们可以将结果应用于经典的Navier-Stokes方程，以使其无法压缩粘性流体。
We consider a family of initial problems for the Navier-Stokes type equations generated by the de Rham complex in ${\mathbb R}^n \times [0,T]$, $n\geq 2$, with a positive time $T$ over a scale weighted anisotropic Hölder spaces. As the weights control the order of zero at the infinity with respect to the space variables for vectors fields under the consideration, this actually leads to initial problems over a compact manifold with the singular conic point at the infinity. We prove that each problem from the family induces Fredholm open injective mappings on elements of the scales. At the step $1$ of the complex we may apply the results to the classical Navier-Stokes equations for incompressible viscous fluid.
