ABSTRACT
In this paper, we consider the two-dimensional isentropic compressible Navier–Stokes equations bounded by a free surface that is under the surface tension and constant exterior pressure. We establish the existence of global strong solution for arbitrary large spherical initial data with initial density away from the vacuum in the case the viscosity coefficients satisfy . In particular, we show that the density is strictly positive and bounded from the above and below in any finite time if the initial density is strictly positive.
Disclosure statement
No potential conflict of interest was reported by the author.
ORCID
Xingwei Zhang http://orcid.org/0000-0003-0066-8767