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

Fabio S. Bemfica; Marcelo M. Disconzi; P. Jameson Graber

doi:10.3934/cpaa.2021068

Article Contents

2021, Volume 20, Issue 9: 2885-2914. Doi: 10.3934/cpaa.2021068

This issue Previous Article Next Article On the Calderon-Zygmund property of Riesz-transform type operators arising in nonlocal equations

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
^* Corresponding author

Received: July 31, 2020

Revised: February 28, 2021

Early access: May 2021

Published: September 2021

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

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Abstract

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.

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

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