Acta mathematica scientia, Series B >
FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY
Received date: 2014-10-26
Revised date: 2014-12-12
Online published: 2016-01-30
Supported by
The research of R.X. Lian is supported by NNSFC(11101145), China Postdoctoral Science Foundation(2012M520360), Doctoral Foundation of North China University of Water Sources and Electric Power(201032), Innovation Scientists and Technicians Troop Construction Projects of Henan Province. The research of J. Liu is supported by NNSFC(11326140 and 11501323), the Doctoral Starting up Foundation of Quzhou University(BSYJ201314 and XNZQN201313).
In this paper, we investigate the free boundary value problem(FBVP) for the cylindrically symmetric isentropic compressible Navier-Stokes equations(CNS) with density-dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.
Ruxu LIAN , Jian LIU . FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY[J]. Acta mathematica scientia, Series B, 2016 , 36(1) : 111 -123 . DOI: 10.1016/S0252-9602(15)30082-5
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