English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the instability of solutions to the relativistic Vlasov--Maxwell systems in two limiting regimes: the classical limit when the speed of light tends to infinity and the quasineutral limit when the Debye length tends to zero. First, in the classical limit, $\varepsilon \to 0$, with $\varepsilon$ being the inverse of the speed of light, we construct a family of solutions that converge initially polynomially fast to a homogeneous solution $\mu$ of Vlasov--Poisson systems in arbitrarily high Sobolev norms, but become of order one away from $\mu$ in arbitrary negative Sobolev norms within time of order $|\log \varepsilon|$. Second, we deduce the invalidity of the quasineutral limit in $L^2$ in arbitrarily short time.

Nonlinear Instability of Vlasov--Maxwell Systems in the Classical and Quasineutral Limits