Local Classical Solutions to the Equations of Relativistic Hydrodynamics

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Volume 14, Issue 3

Yipeng Shi

J. Part. Diff. Eq., 14 (2001), pp. 193-206.

Published online: 2001-08

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Abstract

In this paper, we prove that the convexity of the negative thermodynamical entropy of the equations of relativistic hydrodynamics for ideal gas keeps its invariance under the Lorentz transformation if and only if the local sound speed is less than the light speed in vacuum. Then a symmetric form for the equations of relativistic hydrodynamics is presented and the local classical solution is obtained. Based on this, we prove that the nonrelativistic limit of the local classical solution to the relativistic hydrodynamics equations for relativistic gas is the local classical solution of the Euler equations for polytropic gas.

Keywords

Relativistic hydrodynamics convex entropy local classical solution nonrelativistic limit

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@Article{JPDE-14-193, author = {Yipeng Shi }, title = {Local Classical Solutions to the Equations of Relativistic Hydrodynamics}, journal = {Journal of Partial Differential Equations}, year = {2001}, volume = {14}, number = {3}, pages = {193--206}, abstract = { In this paper, we prove that the convexity of the negative thermodynamical entropy of the equations of relativistic hydrodynamics for ideal gas keeps its invariance under the Lorentz transformation if and only if the local sound speed is less than the light speed in vacuum. Then a symmetric form for the equations of relativistic hydrodynamics is presented and the local classical solution is obtained. Based on this, we prove that the nonrelativistic limit of the local classical solution to the relativistic hydrodynamics equations for relativistic gas is the local classical solution of the Euler equations for polytropic gas.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5479.html} }

TY - JOUR T1 - Local Classical Solutions to the Equations of Relativistic Hydrodynamics AU - Yipeng Shi JO - Journal of Partial Differential Equations VL - 3 SP - 193 EP - 206 PY - 2001 DA - 2001/08 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5479.html KW - Relativistic hydrodynamics KW - convex entropy KW - local classical solution KW - nonrelativistic limit AB - In this paper, we prove that the convexity of the negative thermodynamical entropy of the equations of relativistic hydrodynamics for ideal gas keeps its invariance under the Lorentz transformation if and only if the local sound speed is less than the light speed in vacuum. Then a symmetric form for the equations of relativistic hydrodynamics is presented and the local classical solution is obtained. Based on this, we prove that the nonrelativistic limit of the local classical solution to the relativistic hydrodynamics equations for relativistic gas is the local classical solution of the Euler equations for polytropic gas.

Yipeng Shi . (2001). Local Classical Solutions to the Equations of Relativistic Hydrodynamics. Journal of Partial Differential Equations. 14 (3). 193-206. doi:

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