On properties of solutions of the Cauchy problem for two-dimensional transport equations on a rotating plane

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 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. An explicit asymptotic representation of a smooth solution to transport equations is obtained with the use of the method of stochastic perturbation along characteristics and the process of formation of singularities of solution is analysed on a specific example. It is concluded that the presence of the Coriolis force prevents formation of singularities.