@inbook{da1a3551f7bf4802b90f428c2811d511,
title = "Strong solutions of the Navier-Stokes equations with singular data",
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.",
keywords = "Dirac measure, Global strong solutions, Navier-Stokes equations, Single layer potential, Singular data",
author = "Hideo Kozono and Senjo Shimizu",
note = "Funding Information: 2010 Mathematics Subject Classification. Primary 35Q30; Secondary 76D03, 76D05. Key words and phrases. Navier-Stokes equations, global strong solutions, singular data, Dirac measure, single layer potential. The work of H.K. is partially supported by JSPS Grant in aid for Scientific Research S #16H06339. The work of S.S. is partially supported by JSPS Grant in aid for Scientific Research B #16H03945. Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",
year = "2018",
doi = "10.1090/conm/710/14369",
language = "English",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "163--173",
booktitle = "Contemporary Mathematics",
address = "United States",
}