Spherically symmetric solutions of the multidimensional, compressible, isentropic Euler equations

Schrecker, Matthew

doi:10.1090/tran/7980

Spherically symmetric solutions of the multidimensional, compressible, isentropic Euler equations
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by Matthew R. I. Schrecker PDF

Trans. Amer. Math. Soc. 373 (2020), 727-746 Request permission

Abstract:

In this paper, we prove the existence of finite-energy weak solutions to the compressible, isentropic Euler equations given arbitrary spherically symmetric initial data of finite energy. In particular, we show that the solutions to the spherically symmetric Euler equations obtained in recent works by Chen and Perepelitsa and Chen and Schrecker are weak solutions of the multidimensional, compressible Euler equations. This follows from new uniform estimates made on artificial viscosity approximations up to the origin, removing previous restrictions on admissible test functions and ruling out formation of an artificial boundary layer at the origin. The uniform estimates may be of independent interest concerning the possible rate of blowup of density and velocity at the origin for spherically symmetric flows.

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