Rough solutions of Einstein vacuum equations in CMCSH gauge

2011/12/30 by Qian Wang, Wang, Qian
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1201.0049

arxiv created 2011/12/30 · arxiv updated 2012/01/04

Abstract

In this paper, we consider very rough solutions to Cauchy problem for the Einstein vacuum equations in CMC spacial harmonic gauge, and obtain the local well-posedness result in H^s, s>2. The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric \bg, we manage to implement the commuting vector field approach to prove Strichartz estimate for geometric wave equation \Box_\bg ϕ=0 directly.

Related

• Rough solution for the Einstein Vacuum equations
• On the Well-Posedness of the Vacuum Einstein's Equations
• Local well-posedness of the Einstein-Yang-Mills system in CMCSHGC gauge
• Rough Solutions of the Einstein Constraint Equations
• Sharp Strichartz estimates for the wave equation on a rough background