On the neighborhood of an inhomogeneous stable stationary solution of the Vlasov equation -Case of the Hamiltonian mean-field model
Barré, Julien ; Yamaguchi, Yoshiyuki
HAL, hal-01141165 / Harvested from HAL
Text on HAL
We consider the one-dimensional Vlasov equation with an attractive cosine potential, and its non homogeneous stationary states that are decreasing functions of the energy. We show that in the Sobolev space W 1,p (p > 2) neighborhood of such a state, all stationary states that are decreasing functions of the energy are stable. This is in sharp contrast with the situation for homogeneous stationary states of a Vlasov equation, where a control over strictly more than one derivative is needed to ensure the absence of unstable stationary states in a neighborhood of a reference stationary state
Publié le : 2015-08-06
Classification:  [PHYS]Physics [physics],  [MATH]Mathematics [math] 
@article{hal-01141165,
     author = {Barr\'e, Julien and Yamaguchi, Yoshiyuki},
     title = {On the neighborhood of an inhomogeneous stable stationary solution of the Vlasov equation -Case of the Hamiltonian mean-field model},
     journal = {HAL},
     volume = {2015},
     number = {0},
     year = {2015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01141165}
}

Barré, Julien; Yamaguchi, Yoshiyuki. On the neighborhood of an inhomogeneous stable stationary solution of the Vlasov equation -Case of the Hamiltonian mean-field model. HAL, Tome 2015 (2015) no. 0, . http://gdmltest.u-ga.fr/item/hal-01141165/