Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system

A new proof of partial regularity of solutions to Navier-Stokes equations

“…Let us mention also related interesting works done by Foias and Temam [4], Giga [6] and Sohr and von Wahl [22]. The result of Scheffer was later improved in the stunning result of Caffarelli, Kohn and Nirenberg [1].…”

Regularity criterion via the pressure on weak solutions to the 3D Navier-Stokes equations

“…We are interested in the classical problem of finding sufficient conditions for weak solutions of (1.1) such that they become regular. J. Serrin [10,11] is the pioneer in this direction, and later on, Fabes, Jones and Riviere [4], Giga [5], Sohr [14], Struwe [15] and Takahashi [16] extended and improved Serrin's regularity criterion. They showed that if u is a Leray-Hopf weak solution (see Definition 1.1) of (1.1) belonging to Serrin's class,…”

Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations

“…We apply the following result, summarized from [15], [20], to guarantee short-time smoothness of the solution and thus relieving us from worrying about the legitimacy of the various integral and differential manipulations below.…”