6 papers
Global dynamics of viscous gaseous stars in a physical vacuum
Demin Wang, Jiawen Zhang, Shengguo Zhu
The study of vacuum is important in understanding compressible flows. In particular, physical vacuum, in which the boundary moves with a nontrivial finite normal acceleration, natu…
On a Local Existence Theorem for the Evolution Equation of Viscous Gaseous Stars in a Physical Vacuum
Demin Wang, Jiawen Zhang, Shengguo Zhu
This paper focuses on the free boundary problem of the three-dimensional compressible Navier-Stokes-Poisson equations with degenerate viscosities for self-gravitating viscous gaseo…
Global Regular Solutions of the Compressible Navier-Stokes Equations with Nonlinear Density-Dependent Viscosities and Large Initial Data of Spherical Symmetry
Gui-Qiang G. Chen, Jiawen Zhang, Shengguo Zhu
For the physically important case in which the viscosity coefficients depend on the density through a power law (i.e., with some exponent ), we esta…
Global Well-Posedness of the Vacuum Free Boundary Problem for the Degenerate Compressible Navier-Stokes Equations With Large Data of Spherical Symmetry
Gui-Qiang G. Chen, Jiawen Zhang, Shengguo Zhu
The study of global-in-time dynamics of vacuum is crucial for understanding viscous flows. In particular, physical vacuum, characterized by a moving boundary with nontrivial finite…
Global Regular Solutions of the Degenerate Compressible Navier-Stokes Equations with Large Initial Data of Spherical Symmetry
Gui-Qiang G. Chen, Jiawen Zhang, Shengguo Zhu
A fundamental open problem in the theory of the compressible Navier-Stokes equations is whether regular spherically symmetric flows can develop singularities, such as cavitation or…
Global-in-time Well-posedness of Classical Solutions to the Vacuum Free Boundary Problem for the Viscous Saint-Venant System with Large Data
Xin Zhouping, Zhang Jiawen, Zhu Shengguo
We establish the global well-posedness of classical solutions to the vacuum free boundary problem of the 1-D viscous Saint-Venant system with large data. Since the depth of the…