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On partial regularity for the 3D nonstationary Hall magnetohydrodynamics equations on the plane. (English) Zbl 1336.35287
The purpose of this paper is to study the three-dimensional non-stationary Hall magnetohydrodynamics equation, with an extra quadratically nonlinear Hall term, with homogeneous Dirichlet boundary conditions. The main theorem characterizes the existence of a globally weak solution for an approximate system with given initial conditions. The proof consists of several vector analysis calculations and uses Sobolev embedding, Caccioppoli, Cauchy-Schwartz, Poincaré, Hölder’s and Youngs inequalities, and the Vitali convergence theorem.

MSC:
 35Q35 PDEs in connection with fluid mechanics 35Q85 PDEs in connection with astronomy and astrophysics 76W05 Magnetohydrodynamics and electrohydrodynamics 85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics 35D30 Weak solutions to PDEs
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