Removable time-dependent singularities of solutions to the Stokes equations

Hideo Kozono*, Erika Ushikoshi, Fumitaka Wakabayashi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let Ω⊂RN and let ξ∈Cα([0,T];Ω) for [Formula presented]. We consider the situation that u=u(x,t) is a classical solution of the Stokes equations in ⋃0<t<T(Ω∖{ξ(t)})×{t}, that is, {ξ(t)}0<t<T is regarded as the time-dependent singularities of u in Ω×(0,T). If u behaves around ξ(t) like |u(x,t)|=o(|x−ξ(t)|2−N+(1/α−2)) as x→ξ(t) uniformly in t∈(0,T), then {ξ(t)}0<t<T is a family of removable singularities of u, which implies that u can be extended as a smooth solution in the whole space and time Ω×(0,T).

Original languageEnglish
Pages (from-to)472-489
Number of pages18
JournalJournal of Differential Equations
Publication statusPublished - 2023 Jan 5


  • Bogovskii lemma
  • Moving singularity in time
  • Removable singularity
  • Stokes equations
  • Uniqueness of weak solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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