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Transactions of the American Mathematical Society

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


Author: Matthew R. I. Schrecker
Journal: Trans. Amer. Math. Soc. 373 (2020), 727-746
MSC (2010): Primary 35Q35, 35Q31, 35B44, 35L65, 76N10
DOI: https://doi.org/10.1090/tran/7980
Published electronically: October 1, 2019
MathSciNet review: 4042890
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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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Additional Information

Matthew R. I. Schrecker
Affiliation: University of Wisconsin–Madison, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706
Email: schrecker@wisc.edu

DOI: https://doi.org/10.1090/tran/7980
Received by editor(s): February 7, 2019
Received by editor(s) in revised form: August 1, 2019, August 25, 2019, and August 26, 2019
Published electronically: October 1, 2019
Article copyright: © Copyright 2019 American Mathematical Society