Smoothness of classical solutions to the Vlasov-Maxwell-Landau system near Maxwellians (Q946961)

Smoothness of solutions to the Vlasov-Maxwell-Landau system in a cube \(\left[-\pi,\pi\right]^{3}\) with periodicity boundary conditions is discussed. It is shown that assuming certain bounds of the initial data in suitable norms their finite regularity yields \(C_{\infty}\)-smoothness with respect to space, time and velocity variables in the open time cylinder \(\mathbb{R}_{>0}\times\left[-\pi,\pi\right]^{3}\times\mathbb{R}^{3}\).