The interior regularity of pressure associated with a weak solution to the Navier-Stokes equations with the Navier-type boundary conditions

We prove that if u is a weak solution to the Navier-Stokes system with the Navier-type boundary conditions in Ω×(0,T), satisfying the strong energy inequality in Ω×(0,T) and Serrin's integrability conditions in Ω′×(t1,t2) (where Ω′ is a sub-domain of Ω and 0≤t10 so small that t1+ϵ