On partial regularity for weak solutions to the Navier-Stokes equations
The main goal of this paper is to study the partial regularity for general weak solutions to the Navier-Stokes equations, including the Leray-Hopf weak solution. The author shows that \({\mathcal H}^1(S)= 0\) remains valid for a more general weak solution \(u\) in \(L^\infty((0,T), L^2(\Omega))\cap L^2((0,T), H^1_0(\Omega))\), where \(S\) is the set of possible space-time singular points, \({\mathcal H}^\alpha\) is the \(\alpha\)-dimensional Hausdorff measure. Thus he extends a result of Caffarelli, Kohn and Nirenberg to the general weak solution \(u\).
scientific article; zbMATH DE number 2083556