LOCAL ENERGY ESTIMATES FOR THE MAXWELL–LANDAU–LIFSHITZ SYSTEM AND APPLICATIONS

We study the Maxwell–Landau–Lifshitz system without exchange energy. First, we prove an [Formula: see text] estimate for the linear wave equation and apply this local energy estimate to obtain a bound on the curl of the electromagnetic field, uniformly in time and locally in space. Next, we prove strong convergence results, when the time t tends to ∞ or when the speed of light tends to ∞ (which corresponds to the quasi-stationary approximation). Finally, we establish a stability result with respect to the damping parameter of the Landau–Lifshitz equation.