Partial regularity of solution to generalized Navier-Stokes problem (Q403173)

The author studies the regularity of solutions to the generalized Navier-Stokes equations up to \(C^2\) boundary of the domain \(\Omega \subset \mathbb R^d\) (\(d=2,3\)): \(u_t-\operatorname{div}T(Du,p)+\operatorname{div}(u \otimes u) +\nabla p= f\), \(\operatorname{div}u=0\) in \((0,\tau)\times \Omega\) with the deviatoric part \(\operatorname{div}T(Du,p)\). The Hausdorff measure of a singular set defined as a complement of a set where a solution is Hölder continuous, is estimated. Indirect approach to show partial regularity, for dimension two, is used to get even an empty set of singular points.