Premium
Navier–Stokes equations with degenerate viscosity, vacuum and gravitational force
Author(s) -
Duan Renjun,
Yang Tong,
Zhu Changjiang
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.790
Subject(s) - uniqueness , degenerate energy levels , degeneracy (biology) , gravitation , boundary value problem , mathematics , classical mechanics , isentropic process , compressibility , volume viscosity , mathematical analysis , a priori estimate , conservative force , viscosity , physics , mechanics , quantum mechanics , bioinformatics , biology
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.