ON REGULAR SOLUTIONS AND SINGULARITY FORMATION FOR VLASOV/NAVIER–STOKES EQUATIONS WITH DEGENERATE VISCOSITIES AND VACUUM

Young Pil Choi; Jinwook Jung

doi:10.3934/krm.2022016

ON REGULAR SOLUTIONS AND SINGULARITY FORMATION FOR VLASOV/NAVIER–STOKES EQUATIONS WITH DEGENERATE VISCOSITIES AND VACUUM

Young Pil Choi, Jinwook Jung

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.,

Original language	English
Pages (from-to)	843-891
Number of pages	49
Journal	Kinetic and Related Models
Volume	15
Issue number	5
DOIs	https://doi.org/10.3934/krm.2022016
Publication status	Published - 2022 Oct

Bibliographical note

Funding 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).

Publisher Copyright:
© 2022. Kinetic and Related Modelse.All Rights Reserved.

All Science Journal Classification (ASJC) codes

Numerical Analysis
Modelling and Simulation

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10.3934/krm.2022016

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title = "ON REGULAR SOLUTIONS AND SINGULARITY FORMATION FOR VLASOV/NAVIER–STOKES EQUATIONS WITH DEGENERATE VISCOSITIES AND VACUUM",

abstract = "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.,",

author = "Choi, {Young Pil} and Jinwook Jung",

note = "Funding 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). Publisher Copyright: {\textcopyright} 2022. Kinetic and Related Modelse.All Rights Reserved.",

year = "2022",

month = oct,

doi = "10.3934/krm.2022016",

language = "English",

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N1 - Funding 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). Publisher Copyright: © 2022. Kinetic and Related Modelse.All Rights Reserved.

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N2 - 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.,

AB - 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.,

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ON REGULAR SOLUTIONS AND SINGULARITY FORMATION FOR VLASOV/NAVIER–STOKES EQUATIONS WITH DEGENERATE VISCOSITIES AND VACUUM

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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