The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin[12], which can be used as a phase transition model. Motivated by[9], we aim at extending the work by Danchin-Desjardins[11] to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable Lp-type Besov norms, we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true.
Zhensheng GAO
,
Yan LIANG
,
Zhong TAN
. A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL LP FRAMEWORK[J]. Acta mathematica scientia, Series B, 2019
, 39(6)
: 1639
-1660
.
DOI: 10.1007/s10473-019-0614-7
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