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On the Existence of Global Compactly Supported Weak Solutions of the Vlasov–Poisson System with an External Magnetic Field

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Abstract

We consider the first mixed problem for the Vlasov–Poisson system with an external magnetic field in a domain with piecewise smooth boundary. This problem describes the kinetics of a two-component high-temperature plasma under the influence of a self-consistent electric field and an external magnetic field. The existence of global weak solutions is proved. In the case of a cylindrical domain, sufficient conditions are obtained for the existence of global weak solutions with supports in a strictly internal cylinder; this corresponds to the confinement of high-temperature plasma in a mirror trap.

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Funding

This work was financially supported by the Russian Science Foundation, project 22-21-00392, https://rscf.ru/en/project/22-21-00392/.

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Authors and Affiliations

  1. RUDN University, Moscow, 117198, Russia

    A. L. Skubachevskii

  2. Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia

    A. L. Skubachevskii

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  1. A. L. Skubachevskii
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Correspondence to A. L. Skubachevskii.

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Translated by V. Potapchouck

CONFLICT OF INTEREST. The author of this work declares that he has no conflicts of interest.

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Skubachevskii, A.L. On the Existence of Global Compactly Supported Weak Solutions of the Vlasov–Poisson System with an External Magnetic Field. Diff Equat 59, 1473–1503 (2023). https://doi.org/10.1134/S00122661230110046

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  • DOI: https://doi.org/10.1134/S00122661230110046

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