@inbook{bc1880cc686a47ad8d9562b179e93dda,

title = "On the global well-posedness of some free boundary problem for a compressible barotropic viscous fluid flow",

abstract = "In this paper, we prove a global in time unique existence theorem for the free boundary problem of a compressible barotropic viscous fluid flow without surface tension in the Lp in time and Lq in space framework with 2 < p < ∞ and N < q < ∞ under the assumption that the initial domain is bounded and initial data are small enough and orthogonal to rigid motions. Such global well-posedness was proved by Zajaczkowski in 1993 in the L2 framework, and our result is an extension of his result to the maximal Lp -Lq regularity setting. We use the maximal Lp -Lq regularity theorem for the lin-earlized equations and the exponential stability of the corresponding analytic semigroup, which is a completely different approach than Zajaczkowski (1993).",

author = "Yoshihiro Shibata",

note = "Publisher Copyright: {\textcopyright} 2016 American Mathematical Society.",

year = "2016",

doi = "10.1090/conm/666/13240",

language = "English",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "341--356",

booktitle = "Contemporary Mathematics",

address = "United States",

}