Convergence of the Schrödinger-Poisson system to the Euler equations under the influence of a large magnetic field

Abstract

Abstract.In this paper, we prove the convergence of the current defined from the Schrödinger-Poisson system with the presence of a strong magnetic field toward a dissipative solution of the Euler equations.Mathematics Subject Classification. 76X05, 76N99, 81Q99, 82D10, 35Q40.

Convergence of the Vlasov-Poisson-Fokker-Planck system to the incompressible Euler equations

“…The method has also been applied to show the convergence of Schrödinger-Poisson system to Euler equations, see refs. [17][18][19] for details.…”

Multiplicity and Concentration Results for Fractional Schrödinger-Poisson Equations with Magnetic Fields and Critical Growth

“…ε = 1) and perturbed (i.e. ε > 0 small) Schrödinger-Poisson systems and in absence of magnetic fields have been established, and [16,48,62] for some existence, uniqueness and multiplicity results when A ≡ 0.…”

Incompressible Euler and E-MHD as scaling limits of the Vlasov-Maxwell system

“…In the present paper, we provide a rigorous derivation of these formal limits by using the modulated energy method designed in [Br] for the quasi-neutral limit of the Vlasov-Poisson system. This method has been used in a quantum context in [Pu1], [Pu2] based on the concept of dissipative solutions due to P.-L. Lions [Li]. This method can be seen as a variant of both the relative entropy method [Da], [Ya] and the Hamiltonian energy method by E. Grenier [Gr].…”