## 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.

### MSC:

 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
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### References:

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