Spatially-Periodic Solutions for Evolution Anisotropic Variable-Coefficient Navier-Stokes Equations: I. Existence
8 February 2024
Analysis of PDEs
Sergey E. Mikhailov
Proves existence of periodic solutions to nonstationary anisotropic Navier-Stokes equations
Allows variable viscosity coefficients in space and time
Employs Galerkin method with Bessel operator eigenfunction bases
Covers arbitrary dimension n ≥ 2
Existence of Periodic Solutions for Evolution Anisotropic Navier-Stokes Equations
This paper proves the existence of periodic solutions in arbitrary dimensions to the nonstationary Navier-Stokes equations governing anisotropic fluids, allowing for variable viscosity coefficients in space and time under a relaxed ellipticity condition. A Galerkin method is used with eigenfunction bases for the periodic Bessel potential operator.
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