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

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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).

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages341-356
Number of pages16
DOIs
Publication statusPublished - 2016

Publication series

NameContemporary Mathematics
Volume666
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

ASJC Scopus subject areas

  • Mathematics(all)

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