We analyze the Vlasov equation coupled with the compressible Navier–Stokes equations with degenerate viscosities and vacuum. These two equations are coupled through the drag force which depends on the fluid density and the relative velocity between particle and fluid. We first establish the existence and uniqueness of local-in-time regular solutions with arbitrarily large initial data and a vacuum. We then present sufficient conditions on the initial data leading to the finite-time blowup of regular solutions. In particular, our study makes the result on the finite-time singularity formation for Vlasov/Navier–Stokes equations discussed by Choi [J. Math. Pures Appl.,
|Number of pages||49|
|Journal||Kinetic and Related Models|
|Publication status||Published - 2022 Oct|
Bibliographical noteFunding Information:
Acknowledgments. Y.-P. Choi was supported by National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2017R1C1B2012918 and 2022R1A2C100282011). The work of J. Jung was supported by NRF grant (No. 2019R1A6A1A10073437).
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All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Modelling and Simulation