On the regularity of the pressure of weak solutions of Navier-Stokes equations

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].…”

A direct proof of the Caffarelli-Kohn-Nirenberg theorem

“…Later Lin [9] reproved the Caffarelli-Kohn-Nirenberg theorem by using pressure estimates obtained by Sohr and von Wahl [16]. Afterwards, Ladyzhenskaya and Seregin [6] carried out a more detailed proof of the partial regularity of a suitable weak solution to the Navier-Stokes equations including also the case when a force f is added to the right of (N-S) 2 .…”

Stability of Discrete Stokes Operators in Fractional Sobolev Spaces

“…Scope of the paper. The objective of this paper is to construct approximations for the time-dependent Stokes equations with a source term in L p (0, T ; L q (Ω)) and to prove uniform estimates on the discrete pressure and the time derivative and discrete Laplacian of the discrete velocity that are similar to those proved by Solonnikov [21] and Sohr and von Wahl [20]. To this purpose we construct a finite-element-like approximate Stokes operator and we prove norm equivalences between the scale of norms which it generates and the usual fractional order Sobolev norms for − .…”

“…This estimate has been significantly generalized by Sohr and von Wahl [20] to account for different exponents p ∈ (1, ∞), q ∈ (1, ∞),…”