The relaxation limit of bipolar fluid models. (English) Zbl 1481.35318

Summary: This work establishes the relaxation limit from the bipolar Euler-Poisson system to the bipolar drift-diffusion system, for data so that the latter has a smooth solution. A relative energy identity is developed for the bipolar fluid models, and it is used to show that a dissipative weak solution of the bipolar Euler-Poisson system converges in the high-friction regime to a strong and bounded away from vacuum solution of the bipolar drift-diffusion system.


35Q35 PDEs in connection with fluid mechanics
35Q20 Boltzmann equations
35L65 Hyperbolic conservation laws
35K55 Nonlinear parabolic equations
76A05 Non-Newtonian fluids
76W05 Magnetohydrodynamics and electrohydrodynamics
35B65 Smoothness and regularity of solutions to PDEs
35D30 Weak solutions to PDEs
35D35 Strong solutions to PDEs
82D37 Statistical mechanics of semiconductors
Full Text: DOI arXiv


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