We discuss some results on the Maxwell–Schrödinger system with a nonlinear power-like potential. We prove the local well-posedness in H2(ℝ3)× H3/2ℝ3) and the global existence of finite energy weak solutions. Then we apply these results to the analysis of finite energy weak solutions for Quantum Magnetohydrodynamic systems. Our interest in this problem is motivated by some models arising in quantum plasma dynamics.
The cauchy problem for the maxwell–Schrödinger system with a power-type nonlinearity
Antonelli P.;Marcati P.
2018-01-01
Abstract
We discuss some results on the Maxwell–Schrödinger system with a nonlinear power-like potential. We prove the local well-posedness in H2(ℝ3)× H3/2ℝ3) and the global existence of finite energy weak solutions. Then we apply these results to the analysis of finite energy weak solutions for Quantum Magnetohydrodynamic systems. Our interest in this problem is motivated by some models arising in quantum plasma dynamics.File in questo prodotto:
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