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

Reinhard Farwig, Hideo Kozono, Hermann Sohr

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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.

Original languageEnglish
Pages (from-to)127-150
Number of pages24
JournalJournal of the Mathematical Society of Japan
Issue number1
Publication statusPublished - 2007 Jan
Externally publishedYes



  • Nonhomogeneous data
  • Serrin's class
  • Stokes and navier-stokes equations
  • Very weak solutions

ASJC Scopus subject areas

  • Mathematics(all)

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