10 citations · 63 across the 35 of their papers we have counts for
35 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, which ensures a finite, nontrivial pressure-induced acceleration in the normal…
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…
Development of Implosions of Solutions to the Three-Dimensional Degenerate Compressible Navier-Stokes Equations
Gui-Qiang G. Chen, Lihui Liu, Shengguo Zhu
A fundamental open problem in the theory of the multidimensional compressible Navier-Stokes equations is whether smooth solutions can develop singularities in finite time. For cons…
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 1-D Viscous Saint-Venant System with Large Data
Xin Zhouping, Zhang Jiawen, Zhu Shengguo
We establishes the global existence and uniqueness of classical solutions to the vacuum free boundary problem for the 1-D viscous Saint-Venant system with a general class of large…
Well-posedness of regular solutions for 3-D full compressible Navier-Stokes equations with degenerate viscosities and heat conductivity
Qin Duan, Zhouping Xin, Shengguo Zhu
For the degenerate viscous and heat conductive compressible fluids, the momentum equations and the energy equation are degenerate both in the time evolution and spatial dissipation…
Global Spherically Symmetric Solutions of the Multidimensional Full Compressible Navier-Stokes Equations with Large Data
Gui-Qiang G. Chen, Yucong Huang, Shengguo Zhu
We establish the global-in-time existence of solutions of the Cauchy problem for the full Navier-Stokes equations for compressible heat-conducting flow in multidimensions with init…
Global spherically symmetric solutions to degenerate compressible Navier-Stokes equations with large data and far field vacuum
Yue Cao, Hao Li, Shengguo Zhu
We consider the initial-boundary value problem (IBVP) for the isentropic compressible Navier-Stokes equations (\textbf{CNS}) in the domain exterior to a ball in $(d=2…
Global regular solutions for 1-D degenerate compressible Navier-Stokes equations with large data and far field vacuum
Yue Cao, Hao Li, Shengguo Zhu
In this paper, the Cauchy problem for the one-dimensional (1-D) isentropic compressible Navier-Stokes equations (\textbf{CNS}) is considered. When the viscosity depends on t…
On regular solutions for three-dimensional full compressible Navier-Stokes equations with degenerate viscosities and far field vacuum
Qin Duan, Zhouping Xin, Shengguo Zhu
In this paper, the Cauchy problem for the three-dimensional (3-D) full compressible Navier-Stokes equations (CNS) with zero thermal conductivity is considered. First, when shear an…
Development of singularities in the relativistic Euler equations
Nikolaos Athanasiou, Tianrui Bayles-Rea, Shengguo Zhu
The purpose of this paper is to study the phenomenon of singularity formation in large data problems for classical solutions to the Cauchy problem of the relativistic Euler equatio…
Global Solutions of a Two-Dimensional Riemann Problem for the Pressure Gradient System
Gui-Qiang G. Chen, Qin Wang, Shengguo Zhu
We are concerned with a two-dimensional (-D) Riemann problem for compressible flows modeled by the pressure gradient system that is a -D hyperbolic system of conservation law…
Global mild solutions to three-dimensional magnetohydrodynamic system in Morrey spaces
Feng Liu, Shuai Xi, Shengguo Zhu
In this article, the Cauchy problem of three-dimensional (3-D) incompressible magnetohydrodynamic system was investigated. If the initial norms of the vorticity…
Vanishing Viscosity Limit of the Three-Dimensional Barotropic Compressible Navier-Stokes Equations with Degenerate Viscosities and Far-Field Vacuum
Geng Chen, Gui-Qiang G. Chen, Shengguo Zhu
We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations for barotropic compressible fluids in . When the viscosity coefficients…
On the global-in-time inviscid limit of the 3D isentropic compressible Navier-Stokes equations with degenerate viscosities and vacuum
Yongcai Geng, Yachun Li, Shengguo Zhu
In the recent paper, the global-in-time inviscid limit of the three-dimensional (3D) isentropic compressible Navier-Stokes equations is considered. First, when viscosity coefficien…
On the breakdown of regular solutions with finite energy for 3D degenerate compressible Navier-Stokes equations
Shengguo Zhu
In this paper, the three-dimensional (3D) isentropic compressible Navier-Stokes equations with degenerate viscosities (\textbf{ICND}) is considered in both the whole space and the…
Formation of Singularities and Existence of Global Continuous Solutions for the Compressible Euler Equations
Geng Chen, Gui-Qiang G. Chen, Shengguo Zhu
We are concerned with the formation of singularities and the existence of global continuous solutions of the Cauchy problem for the one-dimensional non-isentropic Euler equations f…
Formation of singularities for the Relativistic Euler equations
Nikolaos Athanasiou, Shengguo Zhu
This paper contributes to the study of large data problems for solutions of the relativistic Euler equations. In the -dimensional spacetime setting, if the initial dat…
Well-posedness of three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities and far field vacuum
Zhouping Xin, Shengguo Zhu
In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations is considered. When viscosity coefficients are given as a constant…
Simplicial volume with -coefficients
Clara Loeh
For primes , we investigate an -version of simplicial volume and compare these invariants with their siblings over other coefficient rings. We will also consider t…
Global well-posedness of regular solutions to the three-dimensional isentropic compressible Navier-Stokes Equations with degenerate viscosities and vacuum
Zhouping Xin, Shengguo Zhu
In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations with degenerate viscosities is considered. By introducing some new…
On classical solutions for viscous polytropic fluids with degenerate viscosities and vacuum
Yachun Li, Ronghua Pan, Shengguo Zhu
In this paper, we consider the three-dimensional isentropic Navier-Stokes equations for compressible fluids with viscosities depending on density in a power law and allowing initia…