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DTSTART;TZID=America/New_York:20230406T093000
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SUMMARY:Rough solutions of the relativistic Euler equations
DESCRIPTION:General Relativity Seminar \nSpeaker: Sifan Yu\, Vanderbilt University \nTitle: Rough solutions of the relativistic Euler equations \nAbstract: I will discuss recent works on the relativistic Euler equations with dynamic vorticity and entropy. We use a new formulation of the equations\, which has geo-analytic structures. In this geometric formulation\, we decompose the flow into geometric “sound-wave part” and “transport-div-curl part”. This allows us to derive sharp results about the dynamics\, including the existence of low-regularity solutions. Then\, I will discuss the results of rough solutions of the relativistic Euler equations and the role that nonlinear geometric optics plays in the framework. Our main result is that the Sobolev norm $H^{2+}$ of the variables in the “wave-part” and the H\”older norm $C^{0\,0+}$ of the variables in the “transport-part” can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption $H^{2+}$ is the optimal result for the variables in the “wave-part.” This talk will include the main ideas of the proof\, as well as a comparison of the relativistic and non-relativistic scenarios.
URL:https://cmsa.fas.harvard.edu/event/gr_4623/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
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