Spatially Periodic Solutions for Evolution Anisotropic Variable‐Coefficient Navier–Stokes Equations: II. Serrin‐Type Solutions
Sergey E. Mikhailov · Mathematical Methods in the Applied Sciences · 2025
ABSTRACT We consider evolution (nonstationary) space‐periodic solutions to the ‐dimensional nonlinear Navier–Stokes equations of anisotropic fluids with the viscosity coefficient tensor variable in space and time and satisfying the relaxed ellipticity condition. Employing the Galerkin algorithm, we prove the existence of Serrin‐type solutions, that is, the weak solutions with velocity in the periodic space , . The solution uniqueness and regularity results are also discussed.