On the solutions for the Kudryashov-Sinelshchikov equation

Abstract The Kudryashov-Sinelshchikov equation models the evolution of the long weakly nonlinear waves, taking into consideration liquid viscosity, inter-phase heat transfer and surface tension. It models also the evolution of nonlinear sound wave propagation in bubbly liquids. Under appropriate assumptions of the coefficients of such equation, in this paper, we prove the well–posedness of the solutions for the Cauchy problem, associated with this equation.