We investigate the nonstationary Navier-Stokes equations for an exterior domain Ω ⊂ R3 in a solution class Ls(0,T; L q(Ω)) of very low regularity in space and time, satisfying Serrin's condition 2/s + 3/q = 1 but not necessarily any differentiability property. The weakest possible boundary conditions, beyond the usual trace theorems, are given by u|∂Ω = g ε Ls(0,T; W-1/q,q(∂Ω)), and will be made precise in this paper. Moreover, we suppose the weakest possible divergence condition k = div u ε Ls (0,T; Lr(Ω)), where 1/3 + 1/q = 1/r.
ASJC Scopus subject areas
- 数学 (全般)