Strong solutions of the Navier-Stokes equations with singular data

Hideo Kozono, Senjo Shimizu

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

We construct strong solutions in the Serrin class of the Navier-Stokes equations with singular data. In 2D case, our results cover the initial vorticity as the Dirac measure and the external force whose support consists of a single point. In 3D case, we can handle the initial vortex sheet supported on the sphere and the singular external force whose support is concentrated on the surface.

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages163-173
Number of pages11
DOIs
Publication statusPublished - 2018 Jan 1
Externally publishedYes

Publication series

NameContemporary Mathematics
Volume710
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Keywords

  • Dirac measure
  • Global strong solutions
  • Navier-Stokes equations
  • Single layer potential
  • Singular data

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Strong solutions of the Navier-Stokes equations with singular data'. Together they form a unique fingerprint.

  • Cite this

    Kozono, H., & Shimizu, S. (2018). Strong solutions of the Navier-Stokes equations with singular data. In Contemporary Mathematics (pp. 163-173). (Contemporary Mathematics; Vol. 710). American Mathematical Society. https://doi.org/10.1090/conm/710/14369