In the framework of the theory of open quantum systems based on completely positive dynamical semigroups, we analyze the time evolution of continuous variable quantum correlations (quantum entanglement and quantum discord) in a system consisting of two coupled bosonic modes interacting with a thermal reservoir. We solve the Markovian master equation which determines the dynamics of the considered system and describe the quantum correlations for Gaussian initial states. Depending on the values of the parameters characterizing the initial state of the system (squeezing parameter, average thermal photon numbers), the coefficients describing the interaction of the system with the environment (temperature, dissipation constant), and on the strength of coupling between the two bosonic modes, we can observe the generation of quantum correlations, their sudden suppression, temporary revivals and suppressions, or an asymptotic decay in the limit of large times.