Weak solutions of the Navier–Stokes equations with non-zero boundary values in an exterior domain satisfying the strong energy inequality

A Note on Prodi–Serrin Conditions for the Regularity of a Weak Solution to the Navier–Stokes Equations

“…In order to work with the weak solutions to problem (1), it is better to study a weak formulation of problem (9). In [24], for all weak solutions to problem (1) Prodi proves the energy equality, that is…”

Initial-boundary value problem of the Navier–Stokes equations in the half space with nonhomogeneous data

“…Further, over the past decade, many mathematicians have focused on studying Navier-Stokes equations with nonhomogeneous boundary data (g = 0) (See [4,7,8,12,13,14,16,17,18,19,25,26,27,28,33,35,44] and the references therein).…”

“…Here, letB In Refs. [7,8,16,17,18,19], rough initial and boundary data were considered for the local data in the time existence of weak or very weak solutions. In Refs.…”

Solvability of the initial–boundary value problem of the Navier–Stokes equations with rough data

“…See [1,4,5,32,40] and references therein for the half space problem. See also [4,5,10,11,12,13,18,19,20,29] and the references therein for the problems in other domains such as whole space, a bounded domain, or exterior domain.…”

“…(∂Ω × (0, T )), α > 1 q (with q > n+2 α+1 ), where g ∈ B s, s 2 q0 (S × (0, T )) means the zero extension of g to S × (−∞, T ) is in B s, s 2 q (S × (−∞, T )). On the other hand, in [1,4,5,10,11,12,13,32,40] a rough boundary data have been considered.…”