  The limiting case of the system of equations of two-dimensional gas dynamics
in the presence of the Coriolis force, which can be obtained under the
assumption of a small pressure, is considered. With this approach, the equation
for the velocity vector (transport equation) is split off from the system and
can be solved separately. Using the method of stochastic perturbation along
characteristics, we obtain an explicit asymptotic representation of a smooth
solution of transport equations and analyze the process of formation of
singularities of solution using a specific example. It is concluded that the
presence of the Coriolis force prevents the singularities formation.
