论文标题
对于$ {\ mathbb r}^3 $的Navier-Stokes方程的常规解决方案的常规解决方案的存在定理
Existence theorems for regular solutions to the Cauchy problem for the Navier-Stokes equations in ${\mathbb R}^3$
论文作者
论文摘要
我们考虑了$ {\ Mathbb r}^3 \ times [0，t] $的Navier-Stokes方程的初始问题，而Bochner-Sobolev类型的特殊构造的功能空间比例为正时$ t $。我们证明，该问题引起了量表每个空间的开放式注射和冲销映射。特别是，这些类的相交给出了唯一性和存在定理，用于平滑解决Navier-Stokes方程的解决方案，以相对于时间和空间变量，在无穷大的情况下具有规定的渐近行为。
We consider the initial problem for the Navier-Stokes equations over ${\mathbb R}^3 \times [0,T]$ with a positive time $T$ over specially constructed scale of function spaces of Bochner-Sobolev type. We prove that the problem induces an open both injective and surjective mapping of each space of the scale. In particular, intersection of these classes gives a uniqueness and existence theorem for smooth solutions to the Navier-Stokes equations for smooth data with a prescribed asymptotic behaviour at the infinity with respect to the time and the space variables.
