TY - JOUR

T1 - Very weak solutions of the Navier-Stokes equations in exterior domains with nonhomogeneous data

AU - Farwig, Reinhard

AU - Kozono, Hideo

AU - Sohr, Hermann

PY - 2007/1

Y1 - 2007/1

N2 - 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.

AB - 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.

KW - Nonhomogeneous data

KW - Serrin's class

KW - Stokes and navier-stokes equations

KW - Very weak solutions

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U2 - 10.2969/jmsj/1180135504

DO - 10.2969/jmsj/1180135504

M3 - Article

AN - SCOPUS:34248594458

SN - 0025-5645

VL - 59

SP - 127

EP - 150

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

IS - 1

ER -