On -stability of strong solutions of the Navier–Stokes equations with the Navier-type boundary conditions

We show that a strong solution u of the Navier–Stokes initial-boundary value problem on the time interval ( 0 , T ) (where 0 < T ≤ ∞ ) is stable in the L 3 -norm, provided u ∈ L 2 ( 0 , T ; W 2 , 2 ( Ω ) ) ∩ L ∞ ( 0 , T ; W σ 1 , 2 ( Ω ) ) . The problem is considered with the so called Navier-type boundary conditions.