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Volume 39, Issue 1
Global Weak Solutions for Compressible Navier-Stokes-Vlasov-Fokker-Planck System

Hai-Liang Li & Ling-Yun Shou

Commun. Math. Res., 39 (2023), pp. 136-172.

Published online: 2022-10

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  • Abstract

The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper. The existence, uniqueness, and regularity of global weak solution to the initial value problem for general initial data are established in spatial periodic domain. Moreover, the long time behavior of the weak solution is analyzed. It is shown that as the time grows, the distribution function of the particles converges to the global Maxwellian, and both the fluid velocity and the macroscopic velocity of the particles converge to the same speed.

  • AMS Subject Headings

35Q30, 35Q84, 82C40

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COPYRIGHT: © Global Science Press

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@Article{CMR-39-136, author = {Li , Hai-Liang and Shou , Ling-Yun}, title = {Global Weak Solutions for Compressible Navier-Stokes-Vlasov-Fokker-Planck System}, journal = {Communications in Mathematical Research }, year = {2022}, volume = {39}, number = {1}, pages = {136--172}, abstract = {

The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper. The existence, uniqueness, and regularity of global weak solution to the initial value problem for general initial data are established in spatial periodic domain. Moreover, the long time behavior of the weak solution is analyzed. It is shown that as the time grows, the distribution function of the particles converges to the global Maxwellian, and both the fluid velocity and the macroscopic velocity of the particles converge to the same speed.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0039}, url = {http://global-sci.org/intro/article_detail/cmr/21081.html} }
TY - JOUR T1 - Global Weak Solutions for Compressible Navier-Stokes-Vlasov-Fokker-Planck System AU - Li , Hai-Liang AU - Shou , Ling-Yun JO - Communications in Mathematical Research VL - 1 SP - 136 EP - 172 PY - 2022 DA - 2022/10 SN - 39 DO - http://doi.org/10.4208/cmr.2021-0039 UR - https://global-sci.org/intro/article_detail/cmr/21081.html KW - Fluid-particle model, compressible Navier-Stokes-Vlasov-Fokker-Planck, hypoellipticity, global existence, large time behavior. AB -

The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper. The existence, uniqueness, and regularity of global weak solution to the initial value problem for general initial data are established in spatial periodic domain. Moreover, the long time behavior of the weak solution is analyzed. It is shown that as the time grows, the distribution function of the particles converges to the global Maxwellian, and both the fluid velocity and the macroscopic velocity of the particles converge to the same speed.

Hai-Liang Li & Ling-Yun Shou. (2022). Global Weak Solutions for Compressible Navier-Stokes-Vlasov-Fokker-Planck System. Communications in Mathematical Research . 39 (1). 136-172. doi:10.4208/cmr.2021-0039
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