Large data problems in fluid dynamics and general relativity

Thesis

In this thesis we contribute to the study of two large data problems within the realm of Hyperbolic Partial Differential Equations. The first result concerns the Relativistic Euler equations, which adequately describe fluid motion in the context of special relativity.

The main result is the provision of a both necessary and sufficient condition on the initial data, uniformly away from vacuum, for the formation of singularities in finite time under the evolution of (1) in the case d = 1. This is joint work with Shengguo Zhu.

The second project developed in this thesis shifts focus from the area of conservation laws to that of mathematical General Relativity. We provide, in joint work with Xinliang An, a trapped surface formation criterion for the Einstein–Maxwell system where the right–hand side corresponds to the Maxwell energy–momentum tensor that models electromagnetic effects.

Authors: Athanasiou, N

• DOI: 10.5287/ora-qxbp8g8aq
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: PDEs; Fluid Dynamics; Athanasiou; General Relativity; Mathematical Analysis; Trapped Surfaces; Partial Differential Equations; Hyperbolic PDEs
• Subjects: Mathematics