An unphysical result for the Landau-Lifshitz equation of motion for a charged particle

An unphysical result for the Landau-Lifshitz equation of motion for a charged particle is presented. The similarity with the Lorentz-Dirac equation is discussed. Indeed the reaction force obtained for the uniform electric field vanishes when the motion is parallel to it in both cases. A discussion of this unphysical result is given and the need for of an expression for the radiation rate of energy for the Landau-Lifshitz theory is emphasized.