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Sufficient conditions for local energy conservation for the compressible Euler system

Volume 168 / 2022

Łukasz Chomienia Colloquium Mathematicum 168 (2022), 171-197 MSC: Primary 35L65; Secondary 35Q31, 76N10. DOI: 10.4064/cm8289-2-2021 Published online: 11 October 2021


We prove a local energy equality for the compressible isentropic Euler equations under the assumptions of Besov regularity in space and Bochner integrability in time. We show that this result can be established for a certain range of exponents which control regularity. We use the Littlewood–Paley decomposition to extend the energy equality to a borderline value of the regularity exponent.


  • Łukasz ChomieniaFaculty of Mathematics, Informatics and Mechanics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland

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