Cambridge Journal of Mathematics

Volume 9 (2021)

Number 2

Well-posedness of free boundary hard phase fluids in Minkowski background and their Newtonian limit

Pages: 269 – 350



Shuang Miao (School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China)

Sohrab Shahshahani (Department of Mathematics and Statistics, University of Massachusetts, Amherst, Mass., U.S.A.)

Sijue Wu (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)


The hard phase model describes a relativistic barotropic irrotational fluid with sound speed equal to the speed of light. In this paper, we prove the local well-posedness for this model in the Minkowski background with free boundary. Moreover, we show that as the speed of light tends to infinity, the solution of this model converges to the solution of the corresponding Newtonian free boundary problem for incompressible fluids. In the appendix we explain how to extend our proof to the general barotropic fluid free boundary problem.

S. Miao was supported by the NSFC grant 12071360 and the Fundamental Research Funds for the Central Universities in China.

S. Shahshahani was supported by the Simons Foundation grant 639284.

S. Wu was supported in part by NSF grant DMS-1764112.

Received 26 July 2020

Published 7 October 2021