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Shock Formation and Vorticity Creation for 3d Euler

Journal Article · · Communications on Pure and Applied Mathematics
DOI:https://doi.org/10.1002/cpa.22067· OSTI ID:2424601
 [1];  [2];  [3]
  1. Department of Mathematics, Princeton University Princeton NJ 08544 USA
  2. Department of Mathematics, UC Davis Davis CA 95616 USA
  3. Courant Institute, New York University New York NY 10012 USA
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Abstract

We analyze the shock formation process for the 3D nonisentropic Euler equations with the ideal gas law, in which sound waves interact with entropy waves to produce vorticity. Building on our theory for isentropic flows in [3, 4], we give a constructive proof of shock formation from smooth initial data. Specifically, we prove that there exist smooth solutions to the nonisentropic Euler equations which form a generic stable shock with explicitly computable blowup time, location, and direction. This is achieved by establishing the asymptotic stability of a generic shock profile in modulated self‐similar variables, controlling the interaction of wave families via: (i) pointwise bounds along Lagrangian trajectories, (ii) geometric vorticity structure, and (iii) high‐order energy estimates in Sobolev spaces. © 2022 Wiley Periodicals LLC.

Research Organization:
Univ. of California, Davis, CA (United States)
Sponsoring Organization:
USDOE
OSTI ID:
2424601
Journal Information:
Communications on Pure and Applied Mathematics, Journal Name: Communications on Pure and Applied Mathematics Journal Issue: 9 Vol. 76; ISSN 0010-3640
Publisher:
Wiley
Country of Publication:
United States
Language:
English

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Related Subjects

Mathematics