The Burgers equation as electrohydrodynamic model in plasma physics

Though our approach is quite general and may be applied to various systems, we only study it in the case of a two dimensional Burgers type equation with a control applied either in

By introducing a Bourgain space associated to the usual KPI equation (re- lated only to the dispersive part of the linear symbol in the KPBI equation), Molinet-Ribaud [14] had

We recall the importance of formula (15) for different topics as Malliavin calculus [Ma97], definition of integral on infinite dimensional surfaces of H [AiMa88], [FePr92],

In such formulation of the original equation we can view (1.7) as a perturbation of the symmetric case and use [3, 7] to obtain the higher order regularity estimates for (1.7) and

established the uniqueness of a stationary measure and its exponential stability for 2D Navier–Stokes equations with a random forcing, white in time and finite-dimensional in

(2.1) The following theorem shows that the approximate controllability is true for any positive time with a control function taking values in a two-dimensional space..

In the present paper, we pursue the idea of spectral methods, but in the frame of spectral collocation methods, where the distribution function is now discretized on a grid of

Math. Crist´ ofani, “Orbital stability of periodic traveling-wave solutions for the log-KdV equation”, J. Kiyashko, and A.V. Pelinovsky, “Sharp bounds on enstrophy growth in