local energy estimates
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2021 ◽  
Vol 59 (4) ◽  
pp. 1918-1947
Author(s):  
Juan Pablo Borthagaray ◽  
Dmitriy Leykekhman ◽  
Ricardo H. Nochetto






2005 ◽  
Vol 02 (03) ◽  
pp. 565-594 ◽  
Author(s):  
JEAN STARYNKÉVITCH

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.





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