A $p$-adic hydrodynamic type equation with two integrals of motion is proposed. It can be considered as a model cascade equation for energy dissipation in fully developed turbulence. Some of special cases of the proposed equation are detailed and it is shown that for a specific choice of parametrs they have stationary solutions that correspond to the 2/3 Kolmogorov-Obukhov law. Possible further studies of the proposed model are discussed.
Categories: math.AP math-ph math.DS math.MP physics.flu-dyn