Transport theory with self-consistent confinement related to the lattice data

The space-time development of a quark-gluon plasma is calculated from a Vlasov equation for the distribution function of quasiparticles with medium dependent masses. At each space-time point the masses are calculated selfconsistently from a gap equation, whose form is determined by the requirement that in thermal equilibrium and for a range of temperatures the energy density of the quasi-particle system is identical to the one from lattice calculations . The numerical solutions of the Vlasov equation display confinement. Relations to effective theories like that by Friedberg Lee and Nambu Jona-Lasinio are established.