论文标题
Navier-Stokes方程中的空间渐近扩展
Spatial asymptotic expansions in the Navier-Stokes equation
论文作者
论文摘要
我们证明，在$ \ mathbb {r}^d $中的粘性不可压缩的流体的Navier-Stokes方程在函数的空间中，允许以$ | x | \ to \ to \ f to的空间渐近扩展为$ | x | \ to \ to \ infty $。该解决方案在分析上取决于初始数据和时间，因此对于任何$ 0 <\ vartheta <π/2 $，它都可以在$ \ Mathbb {c} $中以$ 2 \ vartheta $在零的零态扇区的时间扩展到圆锥扇区。我们通过渐近部件讨论溶液对溶液的近似。
We prove that the Navier-Stokes equation for a viscous incompressible fluid in $\mathbb{R}^d$ is locally well-posed in spaces of functions allowing spatial asymptotic expansions with log terms as $|x|\to\infty$ of any a priori given order. The solution depends analytically on the initial data and time so that for any $0<\vartheta<π/2$ it can be holomorphically extended in time to a conic sector in $\mathbb{C}$ with angle $2\vartheta$ at zero. We discuss the approximation of solutions by their asymptotic parts.
