On regularity of weak solutions for the Navier-Stokes equations in general domains

Let u be a weak solution of the instationary Navier-Stokes equations in a completely general domain omega subset of R3 which additionally satisfies the strong energy inequality. Firstly, we prove that u is regular if the kinetic energy 12 parallel to u(t)parallel to 22 is left-side Holder continuous with Holder exponent 12 and with a sufficiently small Holder seminorm. This result extends the previous ones by several authors [5, 6, 7, 8] in which the domain omega is additionally supposed to be bounded or have the uniform C-2-boundary partial differential omega. Secondly, we show that if u(t)is an element of D(A14) and lim delta -> 0+parallel to A14(u(t-delta)-u(t))parallel to 2

Automated summary

The text discusses the regularity of weak solutions of the unstationary Navier-Stokes equations in a general domain and their relationship with kinetic energy. The study extends previous results and provides specific mathematical expressions to support the findings.