论文标题
部分可观测时空混沌系统的无模型预测
Existence and regularity of steady-state solutions of the Navier-Stokes equations arising from irregular data
论文作者
论文摘要
我们在$ \ mathbb {r}^n _+$，$ n> 2 $中分析了强制不可压缩的固定式Navier-Stokes Flow。在满足帐篷空间比例尺测量的全局集成特性的独特解决方案的存在是为在同质Sobolev空间中的小数据建立的，具有$ s = - \ frac {1} {2} {2} $平滑度。此外，对于任何$ p \ in（1，\ infty）$的任何$ p \，速度字段被证明是局部hölder连续的。我们的方法是基于对不均匀的Stokes系统的分析，我们为此得出了新的可溶性结果，涉及Triebel-lizorkin类中的Dirichlet数据，具有负量的平滑度，并且具有独立的兴趣。
We analyze the forced incompressible stationary Navier-Stokes flow in $\mathbb{R}^n_+$, $n>2$. Existence of a unique solution satisfying a global integrabilty property measured in a scale of tent spaces is established for small data in homogenous Sobolev space with $s=-\frac{1}{2}$ degree of smoothness. Moreover, the velocity field is shown to be locally Hölder continuous while the pressure belongs to $L^p_{loc}$ for any $p\in (1,\infty)$. Our approach is based on the analysis of the inhomogeneous Stokes system for which we derive a new solvability result involving Dirichlet data in Triebel-Lizorkin classes with negative amount of smoothness and is of independent interest.
