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arXiv · 2207.04532

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

Sergey E. Mikhailov
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Abstract

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 $n\in\{2,3,4\}$.

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Sergey E. Mikhailov. 2022-07-10. Stationary Anisotropic Stokes, Oseen, and Navier-Stokes Systems: Periodic Solutions in $\R^n$. https://doi.org/10.1002/mma.9159

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