[2] He solved a number of important problems associated with non-linear partial differential equations that arise in mechanics and physics, initiating the development of several areas in the qualitative theory of dissipative systems.

Chueshov's investigations were related to the well-posedness and asymptotic behavior of the evolutionary von Karman equations, describing nonlinear oscillations of a thin elastic shell under the influence of non-conservative loads.

Chueshov succeeded in developing a new effective method for the analysis of general infinite-dimensional dissipative systems generated by non-linear second-order in time equations.

Chueshov also obtained important results on the uniqueness of invariant measures for stochastic perturbations of the three-dimensional Navier-Stokes equations in thin regions.

[clarification needed] The results provided a fundamental opportunity to use methods of two-dimensional stochastic hydrodynamics to describe the phenomenon of turbulence in some three-dimensional systems.

Together with Professor L. Arnold, he obtained fundamental results on the structure of random attractors, and introduced the important concept of the semi-equilibrium state of a monotone stochastic system.