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
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.
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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