The Existence of Strong Solution for Generalized Navier-Stokes Equations with px-Power Law under Dirichlet Boundary Conditions. (7th December 2021) - Sin, Cholmin
Abstract : In this note, in 2D and 3D smooth bounded domain, we show the existence of strong solution for generalized Navier-Stokes equation modeling by p x -power law with Dirichlet boundary condition under the restriction 3 n / n + 2 n + 2 < p x < 2 n + 1 / n − 1 . In particular, if we neglect the convective term, we get a unique strong solution of the problem under the restriction 2 n + 1 / n + 3 < p x < 2 n + 1 / n − 1, which arises from the nonflatness of domain.