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arXiv · 2207.02951

Energy conservation for weak solutions of incompressible fluid equations: the H\"older case and connections with Onsager's conjecture

Luigi C. Berselli
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Abstract

In this paper we give elementary proofs of energy conservation for weak solutions to the Euler and Navier-Stokes equations in the class of H\"older continuous functions, relaxing some of the assumptions on the time variable (both integrability and regularity at initial time) and presenting them in a unified way. Then, in the final section we prove (for the Navier-Stokes equations) a result of energy conservation in presence of a solid boundary and with Dirichlet boundary conditions. This result seems the first one -- in the viscous case -- with H\"older type assumptions, but without additional assumptions on the pressure.

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Luigi C. Berselli. 2022-07-06. Energy conservation for weak solutions of incompressible fluid equations: the H\"older case and connections with Onsager's conjecture. https://arxiv.org/abs/2207.02951

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