  The modulational instability (MI) and the evolution of weakly nonlinear
two-dimensional (2D) Langmuir wave (LW) packets are studied in an unmagnetized
collisionless plasma with weakly relativistic electron flow. By using a 2D
self-consistent relativistic fluid model and employing the standard
multiple-scale technique, a coupled set of Davey-Stewartson (DS)-like equations
is derived which governs the slow modulation and the evolution of LW packets in
relativistic plasmas. It is found that the relativistic effects favor the
instability of LW envelopes in the k{\theta} plane, where k is the wave number
and {\theta} the angle of modulation. It is also found that as the electron
thermal velocity or {\theta} increases, the growth rate of MI increases with
cutoffs at higher wave numbers of modulation. Furthermore, in the nonlinear
evolution of the DS-like equations, it is seen that with an effect of the
relativistic flow, a Gaussian wave beam collapses in a finite time, and the
collapse can be arrested when the effect of the thermal pressure or the
relativistic flow is slightly relaxed. The present results may be useful to the
MI and the formation of localized LW envelopes in cosmic plasmas with a
relativistic flow of electrons.
