Minimal Acceleration for the Multi-dimensional Isentropic Euler Equations

Minimal Acceleration for the Multi-dimensional Isentropic Euler Equations

On the set of dissipative solutions to the multi-dimensional isentropic Euler equations, we introduce a quasi-order by comparing the acceleration at all time. This quasi-order is continuous with respect to a suitable notion of convergence of dissipative solutions. We establish the existence of minim...

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Veröffentlicht in:Archive for rational mechanics and analysis 2023-06, Vol.247 (3), p.35, Article 35
1. Verfasser: Westdickenberg, Michael
Format: Artikel
Sprache:eng
Schlagworte:
Classical Mechanics
Complex Systems
Digital Object Identifier
Dissipation
Energy
Entropy
Euler-Lagrange equation
Eulers equations
Fluid- and Aerodynamics
Inequality
Mathematical analysis
Mathematical and Computational Physics
Physics
Physics and Astronomy
Spacetime
Theoretical
Velocity
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Beschreibung
Zusammenfassung:On the set of dissipative solutions to the multi-dimensional isentropic Euler equations, we introduce a quasi-order by comparing the acceleration at all time. This quasi-order is continuous with respect to a suitable notion of convergence of dissipative solutions. We establish the existence of minimal elements. Minimizing the acceleration amounts to selecting dissipative solutions that are as close to being a weak solution as possible.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-023-01864-x