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May  2020, 19(5): 2737-2750. doi: 10.3934/cpaa.2020119

Asymptotic analysis for 1D compressible Navier-Stokes-Vlasov equations

 1 School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China 2 College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China 3 School of Mathematics, Northwest University, Xi'an 710127, China

* Corresponding author

Received  April 2019 Revised  October 2019 Published  March 2020

Fund Project: H. Cui is supported by the National Natural Science Foundation of China (Grant No. 11971183, 11601164 and 11571380), the Natural Science Foundation of Fujian Province of China (Grant No. 2017J05007). W. Wang is supported by the National Natural Science Foundation of China (Grant No. 11871341, 11671150 and 11571231). L. Yao is supported by the National Natural Science Foundation of China (Grant No. 11571280 and 11931013), Natural Science Basic Research Program of Shaanxi (Program No. 2019JC-26) and FANEDD #201315

In this paper, we study the asymptotic analysis of 1D compressible Navier-Stokes-Vlasov equations. By taking advantage of the one space dimension, we obtain the hydrodynamic limit for compressible Navier-Stokes-Vlasov equations with the pressure $P(\rho) = A\rho^{\gamma}$ $(\gamma>1)$. The proof relies on weak convergence method.

Citation: Haibo Cui, Wenjun Wang, Lei Yao. Asymptotic analysis for 1D compressible Navier-Stokes-Vlasov equations. Communications on Pure & Applied Analysis, 2020, 19 (5) : 2737-2750. doi: 10.3934/cpaa.2020119
References:

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