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&#8712[1, &#8734], 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.