Local existence and uniqueness in Sobolev spaces for first-order conformal causal relativistic viscous hydrodynamics

Fabio Sperotto Bemfica; Marcelo Mendes Disconzi; Casey Rodriguez; Yuanzhen Shao

doi:10.3934/cpaa.2021069

Article Contents

2021, Volume 20, Issue 6: 2279-2290. Doi: 10.3934/cpaa.2021069

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Local existence and uniqueness in Sobolev spaces for first-order conformal causal relativistic viscous hydrodynamics

1.
Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, Natal, RN 59072-970, Brazil
2.
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA
3.
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA
4.
Department of Mathematics, The University of Alabama, Tuscaloosa, AL 35487-0350, USA

^* Corresponding author
^* Corresponding author

Received: July 31, 2020

Revised: January 31, 2021

Early access: April 2021

Published: June 2021

The first author is supported by a Discovery grant administered by Vanderbilt University The second author is supported by a Sloan Research Fellowship, NSF grant # 1812826, a Dean's Faculty Fellowship and a Discovery grant administered by Vanderbilt University. The third author is supported by NSF Postdoctoral Research Fellowship DMS-1703180

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Abstract

In this manuscript, we study the theory of conformal relativistic viscous hydrodynamics introduced in [4], which provided a causal and stable first-order theory of relativistic fluids with viscosity. Local existence and uniqueness of solutions to its equations of motion have been previously established in Gevrey spaces. Here, we improve this result by proving local existence and uniqueness of solutions in Sobolev spaces.

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Mathematics Subject Classification: Primary: 35Q75; Secondary: 35Q35, 35Q31.

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