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This paper is devoted to the investigation of the 2D incompressible electrohydrodynamics system by the artificial compressibility method. We first introduce a family of perturbed compressible electrohydrodynamics, which approximate the incompressible electrohydrodynamics as the compressibility parameter is sent to zero. Then we prove the unique existence and convergence of solutions for the perturbed compressible electrohydrodynamics system to the solutions of the incompressible electrohydrodynamics system.

Approximation of the 2D incompressible electrohydrodynamics system by the artificial compressibility method