Periodic Solutions in ${\mathbb{R}}^n$ for Stationary Anisotropic Stokes and Navier-Stokes Systems

Abstract

First, the solution uniqueness and existence of a stationary anisotropic (linear) Stokes system with constant viscosity coefficients in a compressible framework on $n$-dimensional flat torus are analysed in a range of periodic Sobolev (Bessel-potential) spaces. By employing the Leray-Schauder fixed point theorem, 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. Then the solution regularity results for stationary anisotropic Navier-Stokes system on torus are established.

15 pages, corrected

Cited by in corpus (1)

• Stationary Anisotropic Stokes, Oseen, and Navier-Stokes Systems: Periodic Solutions in ${\mathbb{R}}^n$