Nonlinear instability of Vlasov-Maxwell systems in the classical and quasineutral limits

Daniel Han-Kwan, Toan T. Nguyen

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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, ε → 0, with ε being the inverse of the speed of light, we construct a family of solutions that converge initially polynomially fast to a homogeneous solution μ of Vlasov-Poisson systems in arbitrarily high Sobolev norms, but become of order one away from μ in arbitrary negative Sobolev norms within time of order |log ε|. Second, we deduce the invalidity of the quasineutral limit in L2 in arbitrarily short time.

Original languageEnglish (US)
Pages (from-to)3444-3466
Number of pages23
JournalSIAM Journal on Mathematical Analysis
Volume48
Issue number5
DOIs
StatePublished - Jan 1 2016

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Quasi-neutral Limit
Nonlinear Instability
Light velocity
Maxwell System
Classical Limit
Tend
Vlasov-Poisson System
Norm
Deduce
Limiting
Infinity
Converge
Zero
Arbitrary

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Nonlinear instability of Vlasov-Maxwell systems in the classical and quasineutral limits. / Han-Kwan, Daniel; Nguyen, Toan T.

In: SIAM Journal on Mathematical Analysis, Vol. 48, No. 5, 01.01.2016, p. 3444-3466.

Research output: Contribution to journalArticle

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AB - 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, ε → 0, with ε being the inverse of the speed of light, we construct a family of solutions that converge initially polynomially fast to a homogeneous solution μ of Vlasov-Poisson systems in arbitrarily high Sobolev norms, but become of order one away from μ in arbitrary negative Sobolev norms within time of order |log ε|. Second, we deduce the invalidity of the quasineutral limit in L2 in arbitrarily short time.

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