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

In: Integral Methods in Science and Engineering

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  • S. E. Mikhailov

    (Brunel University London)

Abstract

First, the solution uniqueness and existence of a stationary, anisotropic (linear) Stokes system with constant viscosity coefficients in a compressible framework are analysed on n-dimensional flat torus in a range of periodic Sobolev (Bessel-potential) spaces. By employing the Leray-Schauder fixed point theorem, the linear results are used to show existence of solution to the stationary anisotropic (non-linear) Navier-Stokes incompressible system on torus in a periodic Sobolev space for n ∈{2, 3}. Then the solution regularity results for stationary anisotropic Navier-Stokes system on torus are established for n ∈{2, 3}

Suggested Citation

  • S. E. Mikhailov, 2022. "Periodic Solutions in ℝ n $${\mathbb R}^n$$ for Stationary Anisotropic Stokes and Navier-Stokes Systems," Springer Books, in: Christian Constanda & Bardo E.J. Bodmann & Paul J. Harris (ed.), Integral Methods in Science and Engineering, chapter 0, pages 227-243, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-07171-3_16
    DOI: 10.1007/978-3-031-07171-3_16
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