We consider a free interface problem for the Navier-Stokes equations. We obtain local in time unique existence of solutions to this problem for any initial data and external forces, and global in time unique existence of solutions for sufficiently small initial data. Thanks to global in time maximal regularity of the linearized problem, we can prove a global in time existence and uniqueness theorem by the contraction mapping principle.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-29,
author = {Senjo Shimizu},
title = {Maximal regularity and viscous incompressible flows with free interface},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {471-480},
zbl = {1154.35480},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-29}
}
Senjo Shimizu. Maximal regularity and viscous incompressible flows with free interface. Banach Center Publications, Tome 83 (2008) pp. 471-480. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-29/