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| In this talk, we consider the Cauchy problem of the Euler-Maxwell system. The Euler-Maxwell system describes the dynamics of compressible electrons in plasma physics under the interaction of the magnetic and electric fields via the Lorentz force.
Our purpose is to study the large-time behavior of solutions to the initial value problem for the Euler-Maxwell system in whole space. This system verifies the decay property of the regularity-loss type.
Under smallness condition on the initial perturbation, we show that the solution to the problem exists globally in time and converges to the equilibrium state (and the stationary solution). Moreover we derive the corresponding convergence rate of the solutions.The key to the proof of our main theorems are to derive a priori estimates of solutions by using the energy method. |
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