September  2021, 20(9): 2885-2914. doi: 10.3934/cpaa.2021068

Local well-posedness in Sobolev spaces for first-order barotropic causal relativistic viscous hydrodynamics

1. 

Universidade Federal do Rio Grande do Norte, Campus Universitário Lagoa Nova, Natal, RN, 59078-970, Brazil

2. 

Vanderbilt University, 1326 Stevenson Center Ln, Nashville, TN, 37240, USA

3. 

Baylor University, Sid Richardson Building, 1410 S. 4th Street, Waco, TX 76706, USA

* Corresponding author

Received  August 2020 Revised  March 2021 Published  September 2021 Early access  June 2021

Fund Project: The second author is partially supported by a Sloan Research Fellowship provided by the Alfred P. Sloan foundation, by NSF grant DMS-1812826, and by a Discovery grant administered by Vanderbilt University, and from a Dean's Faculty Fellowship. The third author is partially supported by NSF grant DMS-1905449

We study the theory of relativistic viscous hydrodynamics introduced in [14, 58], which provided a causal and stable first-order theory of relativistic fluids with viscosity in the case of barotropic fluids. The local well-posedness of its equations of motion has been previously established in Gevrey spaces. Here, we improve this result by proving local well-posedness in Sobolev spaces.

Citation: Fabio S. Bemfica, Marcelo M. Disconzi, P. Jameson Graber. Local well-posedness in Sobolev spaces for first-order barotropic causal relativistic viscous hydrodynamics. Communications on Pure & Applied Analysis, 2021, 20 (9) : 2885-2914. doi: 10.3934/cpaa.2021068
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