论文标题
固定各向异性Stokes，Oseen和Navier-Stokes Systems：$ \ r^n $的定期解决方案
Stationary Anisotropic Stokes, Oseen, and Navier-Stokes Systems: Periodic Solutions in $\R^n$
论文作者
论文摘要
首先，在一系列定期的Sobolev（Bessel-Potential）空间上分析了固定各向异性（线性）Stokes和具有恒定粘度系数的通用OSEEN系统的解决方案唯一性，存在和规律性。通过Galerkin算法，使用线性结果显示了对固定的sobolev空间中任何$ n \ ge 2 $的固定各向异性（非线性）Navier-Stokes不可压缩系统的解决方案。然后，以\ {2,3,4 \} $为$ n \建立了固定各向异性Navier-Stokes系统的解决方案唯一性和规律性结果。
First, the solution uniqueness, existence and regularity for stationary anisotropic (linear) Stokes and generalised Oseen systems with constant viscosity coefficients in a compressible framework are analysed in a range of periodic Sobolev (Bessel-potential) spaces on $n$-dimensional flat torus. By the Galerkin algorithm, the linear results are employed to show existence of solution to the stationary anisotropic (non-linear) Navier-Stokes incompressible system on torus in a periodic Sobolev space for any $n\ge 2$. Then the solution uniqueness and regularity results for stationary anisotropic Navier-Stokes system on torus are established for $n\in\{2,3,4\}$.
