Conserved Quantities and Regularity in Fluid Dynamics

Wiedemann E (2026)


Publication Type: Book chapter / Article in edited volumes

Publication year: 2026

Publisher: Birkhauser

Series: Necas Center Series

Book Volume: Part F1294

Pages Range: 257-285

DOI: 10.1007/978-3-032-02319-3_5

Abstract

Conserved or dissipated quantities, like energy or entropy, are at the heart of the study of many classes of time-dependent PDEs in connection with fluid mechanics. This is the case, for instance, for the Euler and Navier-Stokes equations, for systems of conservation laws, and for transport equations. In all these cases, a formally conserved quantity may no longer be constant in time for a weak solution at low regularity. The delicate interplay between regularity and conservation of the respective quantity relates to renormalisation in the DiPerna-Lions theory of transport and continuity equations, and to Onsager’s conjecture in the realm of ideal incompressible fluids. We will review the classical commutator methods of DiPerna-Lions and Constantin-E-Titi, and then proceed to more recent results.

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How to cite

APA:

Wiedemann, E. (2026). Conserved Quantities and Regularity in Fluid Dynamics. In (pp. 257-285). Birkhauser.

MLA:

Wiedemann, Emil. "Conserved Quantities and Regularity in Fluid Dynamics." Birkhauser, 2026. 257-285.

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