ИСТИНА

A system of equations of two-dimensional shallow water above the rough bottom is considered. An overdetermined system of equations for determining the functions forming the conservation laws of the system of shallow water equations is obtained. The general form of the solution of the overdetermined system is found. The general classification equation is given. The system of equations of two-dimensional shallow water above the rough bottom for any profile of the bottom is shown to have no more than the nine-dimensional space of the hydrodynamic conservation laws. The new conservation law, supplementary to the basic conservation law, is obtained (as in one-dimensional case). All of the hydrodynamic conservation laws have found for all possible bottom profiles.