arXiv subjects

Zeming Hao

Publications and source records attributed to Zeming Hao.

3 recordsLinked to original sources

arXiv2024

Well-posedness for the free boundary barotropic fluid model in general relativity

In the framework of general relativity, the dynamics of a general barotropic fluid are coupled to the Einstein equations, which govern the structure of the underlying spacetime. We establish a priori estimates and well-posedness in Sobolev spaces for this model with a free boundary. Within the frame parallel-transported by the fluid velocity, we decompose the fluid and geometric quantities. The fluid components are estimated via a coupled interior-boundary wave equation, while the geometric quantities are analyzed through the Bianchi equations. Compared to a previous work, the results in present paper allow general equations of state and non-zero vorticities.

math.AP↗

arXiv2023

On stability analysis for steady states of the free boundary hard phase model in general relativity

The hard phase model describes a relativistic barotropic fluid with sound speed equal to the speed of light. In the framework of general relativity, the motion of the fluid is coupled to the Einstein equations which describe the structure of the underlying spacetime. This model with free boundary admits a $1$-parameter family of steady states with spherical symmetry. In this work, for perturbations within spherical symmetry, we study the stability and instability of this family. We prove that the linearized operator around steady states with large central densities admits a growing mode, while such growing modes do not exist for steady states with small central densities. Based on the linear analysis, we further demonstrate a dynamical nonlinear instability for steady states with large central densities. The proof relies on a spectral analysis of the linearized operator and an a priori estimate on the full nonlinear free boundary problem.

math.AP↗

arXiv2023

On nonlinear instability of liquid Lane-Emden stars

We establish a dynamical nonlinear instability of liquid Lane-Emden stars in $\mathbb{R}^{3}$ whose adiabatic exponents take values in $[1,\frac43)$. Our proof relies on a priori estimates for the free boundary problem of a compressible self-gravitating liquid, as well as a quantitative analysis of the competition between the fastest linear growing mode and the source.

math.AP↗