Stability of Navier-Stokes-Oseen flows

This paper studies the stability of a weak mild solution of the Navier–Stokes–Oseen equations in the solenoidal Lorentz space $ L^{3}_{\sigma, {{{\rm{w}}}}} $. Our approach relies on dual space pair and suitable estimates in our setting for the Oseen semigroup. Therefore, we get a new result for the stability of a weak mild solution following the initial datum and external force.