Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations
- 13 December 1999
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 13 (1) , 249-255
- https://doi.org/10.1088/0951-7715/13/1/312
Abstract
We study the local equation of energy for weak solutions of three-dimensional incompressible Navier-Stokes and Euler equations. We define a dissipation term D (u ) which stems from an eventual lack of smoothness in the solution u . We give in passing a simple proof of Onsager's conjecture on energy conservation for the three-dimensional Euler equation, slightly weakening the assumption of Constantin et al . We suggest calling weak solutions with non-negative D (u ) `dissipative'.Keywords
This publication has 5 references indexed in Scilit:
- Energy dissipation without viscosity in ideal hydrodynamics I. Fourier analysis and local energy transferPhysica D: Nonlinear Phenomena, 1994
- Onsager's conjecture on the energy conservation for solutions of Euler's equationCommunications in Mathematical Physics, 1994
- An inviscid flow with compact support in space-timeThe Journal of Geometric Analysis, 1993
- Statistical hydrodynamicsIl Nuovo Cimento (1869-1876), 1949
- Sur le mouvement d'un liquide visqueux emplissant l'espaceActa Mathematica, 1934