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

S. E. Mikhailov ()
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S. E. Mikhailov: Brunel University London

Chapter Chapter 16 in Integral Methods in Science and Engineering, 2022, pp 227-243 from Springer

Abstract: 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}

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-07171-3_16

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DOI: 10.1007/978-3-031-07171-3_16

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