Regularity of solutions to non-stationary Navier–Stokes equations

Abstract

This paper covers a non-stationary system of Navier–Stokes equations for incompressible fluids. A regularized problem is considered that factors in the velocity field being relaxed to a solenoidal field; this problem is used to prove the pressure function exists almost everywhere in the domain for the Hopf class solutions. The proposed regularization proves there exist more regular weak solutions to the initial problem that do not impose smallness restrictions on the input data. The theorem of uniqueness is proven for the 2D case.