Work

Singularity formation for the relativistic Euler equations of Chaplygin gases in Schwarzschild spacetime

Year: 2024

Type: article

Abstract: We study the formation of singularities of smooth solutions to the relativistic Euler equations of Chaplygin gases in Schwarzschild spacetime. The system is in the spherically symmetric form, and its coefficients and nonhomogeneous terms contain a parameter reflecting the mass of the black hole, which makes it highly nonlinear and complicated. To overcome the influence of the mass parameter of black hole, we introduce a pair of suitable auxiliary variables related to it and derive their characteristic decompositions to establish the estimates of the smooth solution. We show that, for a kind of initial data, the smooth solution develops singularity in finite time and the mass‐energy density itself approaches infinity at the blowup point.

Source: Studies in Applied Mathematics

DOI: 10.1111/sapm.12775

Authors: Yanbo Hu, Houbin Guo

Institutions: Zhejiang University of Science and Technology, Hangzhou Normal University

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Natural Science Foundation of China

Awards: G391286240, G5594291468