Spatially-Periodic Solutions for Evolution Anisotropic Variable-Coefficient Navier–Stokes Equations: I. Weak Solution Existence

Sergey E. Mikhailov ()
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Sergey E. Mikhailov: Department of Mathematics, Brunel University London, Uxbridge UB8 3PH, UK

Mathematics, 2024, vol. 12, issue 12, 1-27

Abstract: We consider evolution (non-stationary) spatially-periodic solutions to the n -dimensional non-linear Navier–Stokes equations of anisotropic fluids with the viscosity coefficient tensor variable in spatial coordinates and time and satisfying the relaxed ellipticity condition. Employing the Galerkin algorithm with the basis constituted by the eigenfunctions of the periodic Bessel-potential operator, we prove the existence of a global weak solution.

Keywords: partial differential equations; evolution Navier–Stokes equations; anisotropic Navier–Stokes equations; spatially periodic solutions; variable coefficients; relaxed ellipticity condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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