Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 14
192
Views
7
CrossRef citations to date
0
Altmetric
Articles

The limits of Riemann solutions to the relativistic van der Waals fluid

ORCID Icon &
Pages 2989-3010 | Received 28 Mar 2019, Accepted 10 Dec 2019, Published online: 24 Dec 2019
 

Abstract

By a Riemann problem, we identify and analyze the phenomena of concentration and cavitation and the formation of delta-shock waves and vacuum states in solutions to the relativistic van der Waals fluid as the pressure and molecular excluded volume drop to zero simultaneously. Particularly, the geometric properties of elementary wave curves and the formation process of delta shocks and vacuums, influenced by the parameter of pressure perturbation ε and the van der Waals excluded volume b, are characterized and clarified completely. It is rigorously shown that the Riemann solution of the relativistic van der Waals fluid containing two shocks and two-rarefaction waves respectively tend to the delta-shock solution and vacuum state to the pressureless relativistic Euler equations as both pressure and molecular excluded volume vanish.

COMMUNICATED BY:

AMS CLASSIFICATIONS:

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by Yunnan Applied Basic Research Projects [grant number 2018FD015]; Scientific Research Foundation Project of Yunnan Education Department [grant number 2018JS150]; Science and Technology Foundation of Hebei Education Department [grant number QN2018307]; Natural Science Foundation of Hebei Province [grant number A2019105110].

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,361.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.