Energy conservation for weak solutions of incompressible fluid equations: the H\'older case and connections with Onsager's conjecture
- Resource Type
- Working Paper
- Authors
- Berselli, Luigi C.
- Source
- Subject
- Mathematics - Analysis of PDEs
35Q30
- Language
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.
Comment: 18 pages