@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} }