Volume 2, Issue 4
Dynamic Instability of Stationary Solutions to the Nonlinear Vlasov Equations

SUN-HO CHOI AND SEUNG-YEAL HA

Int. J. Numer. Anal. Mod. B, 2 (2011), pp. 415-421

Published online: 2011-02

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  • Abstract
We present the dynamic instability of smooth compactly supported stationary solutions to the nonlinear Vlasov equations with self-consistent attractive forces. For this, we explicitly construct a one-parameter family of perturbed solutions via the method of the Galilean boost. Initially, these perturbations can be close to the given stationary solution as much as possible in any L^p-norm, p∈[1, ∞], and have the same local mass density profile as a stationary solution, but a different bulk velocity profile. At the macroscopic level, these perturbations correspond to the traveling waves with compact supports. However in finite-time, the phase-space supports of these perturbations will be disjoint from the support of the given stationary solution. This establishes the dynamic instability of stationary solutions in any L^p-norm.
  • AMS Subject Headings

92D25 74A25 76N10

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COPYRIGHT: © Global Science Press

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@Article{IJNAMB-2-415, author = {SUN-HO CHOI AND SEUNG-YEAL HA}, title = {Dynamic Instability of Stationary Solutions to the Nonlinear Vlasov Equations}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2011}, volume = {2}, number = {4}, pages = {415--421}, abstract = {We present the dynamic instability of smooth compactly supported stationary solutions to the nonlinear Vlasov equations with self-consistent attractive forces. For this, we explicitly construct a one-parameter family of perturbed solutions via the method of the Galilean boost. Initially, these perturbations can be close to the given stationary solution as much as possible in any L^p-norm, p∈[1, ∞], and have the same local mass density profile as a stationary solution, but a different bulk velocity profile. At the macroscopic level, these perturbations correspond to the traveling waves with compact supports. However in finite-time, the phase-space supports of these perturbations will be disjoint from the support of the given stationary solution. This establishes the dynamic instability of stationary solutions in any L^p-norm.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/321.html} }
TY - JOUR T1 - Dynamic Instability of Stationary Solutions to the Nonlinear Vlasov Equations AU - SUN-HO CHOI AND SEUNG-YEAL HA JO - International Journal of Numerical Analysis Modeling Series B VL - 4 SP - 415 EP - 421 PY - 2011 DA - 2011/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/321.html KW - Dynamic instability KW - Galilean boost KW - stationary solution KW - Vlasov-Poisson system KW - Vlasov-Yukawa system KW - Euler-Poisson system AB - We present the dynamic instability of smooth compactly supported stationary solutions to the nonlinear Vlasov equations with self-consistent attractive forces. For this, we explicitly construct a one-parameter family of perturbed solutions via the method of the Galilean boost. Initially, these perturbations can be close to the given stationary solution as much as possible in any L^p-norm, p∈[1, ∞], and have the same local mass density profile as a stationary solution, but a different bulk velocity profile. At the macroscopic level, these perturbations correspond to the traveling waves with compact supports. However in finite-time, the phase-space supports of these perturbations will be disjoint from the support of the given stationary solution. This establishes the dynamic instability of stationary solutions in any L^p-norm.
SUN-HO CHOI AND SEUNG-YEAL HA. (2011). Dynamic Instability of Stationary Solutions to the Nonlinear Vlasov Equations. International Journal of Numerical Analysis Modeling Series B. 2 (4). 415-421. doi:
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