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Theses

On the Constraint Equations in General Relativity

Abstract : The long-term goal of my work is to find a viable alternative to the conformal method, which would allow us to better understand the geometry of the space of solutions of the constraint equations. The advantage of Maxwell's model (the drift model) is the presence of additional parameters. Its downside, however, is that it proves to be much more difficult from an analytic standpoint. My thesis is structued in two parts: a. Existence under suitable smallness conditions. We show that Maxwell's system is sufficiently reasonable: it can be solved even given the presence of focusing non linearities. We prove this under smallness conditions of its coefficients, and in dimensions 3,4 and 5. An immediate consequence is that the set of solutions is non-empty. b. Stability. We verify that the solutions of the system are stable: this result holds in dimensions 3,4 and 5, when the metric is conformally flat and the drift is small
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  • HAL Id : tel-02463842, version 1

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Caterina Valcu. On the Constraint Equations in General Relativity. Analysis of PDEs [math.AP]. Université de Lyon, 2019. English. ⟨NNT : 2019LYSE1180⟩. ⟨tel-02463842⟩

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