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The Diffusive Limit of the Bipolar Vlasov–Poisson–Boltzmann Equations


In this work, we first prove the existence of the classic solutions to the dimensionless bipolar Vlasov–Poisson–Boltzmann equations by employing hypocoercive properties of the linear Boltzmann operators. Based on the uniform estimates and employing the Ohm’s law, two fluids Navier–Stokes–Poisson system is derived from the dimensionless Vlasov–Poisson–Boltzmann equations.

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No data or code were generated or used during the study. The only model used in this work can be find in the reference.


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The first author was supported by Chongqing University of Posts and Telecommunications startup fund (Grant No. A2018-128). The second author was supported by the National Natural Science Foundation of China (Grant Nos. 11271305, 11531010). The third author was supported by National Natural Science Foundation of China (Grant No. 11901537).

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Correspondence to Xu Zhang.

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Communicated by Clement Mouhot.

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Tong, L., Tan, Z. & Zhang, X. The Diffusive Limit of the Bipolar Vlasov–Poisson–Boltzmann Equations. J Stat Phys 188, 2 (2022).

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