TY - JOUR
T1 - Navier-Stokes equations with degenerate viscosity, vacuum and gravitational force
AU - Duan, Renjun
AU - Yang, Tong
AU - Zhu, Changjiang
PY - 2007/2
Y1 - 2007/2
N2 - The global existence of weak solutions to the compressible Navier-Stokes equations with vacuum attracts many research interests nowadays. For the isentropic gas, the viscosity coefficient depends on density function from physical point of view. When the density function connects to vacuum continuously, the vacuum degeneracy gives some analytic difficulties in proving global existence. In this paper, we consider this case with gravitational force and fixed boundary condition. By giving a series of a priori estimates on the solution coping with the degeneracy of vacuum, gravitational force and boundary effect, we give global existence and uniqueness results similar to the case without force and boundary. Copyright © 2006 John Wiley & Sons, Ltd.
AB - The global existence of weak solutions to the compressible Navier-Stokes equations with vacuum attracts many research interests nowadays. For the isentropic gas, the viscosity coefficient depends on density function from physical point of view. When the density function connects to vacuum continuously, the vacuum degeneracy gives some analytic difficulties in proving global existence. In this paper, we consider this case with gravitational force and fixed boundary condition. By giving a series of a priori estimates on the solution coping with the degeneracy of vacuum, gravitational force and boundary effect, we give global existence and uniqueness results similar to the case without force and boundary. Copyright © 2006 John Wiley & Sons, Ltd.
KW - A priori estimates
KW - Global existence
KW - Navier-Stokes equations
KW - Vacuum
UR - http://www.scopus.com/inward/record.url?scp=33846490299&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-33846490299&origin=recordpage
U2 - 10.1002/mma.790
DO - 10.1002/mma.790
M3 - RGC 21 - Publication in refereed journal
VL - 30
SP - 347
EP - 374
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
SN - 0170-4214
IS - 3
ER -