Davit HARUTYUNYAN

Research project

Inertial manifold approach in the ergodic theory of stochastic PDEs

The ergodic theory of stochastic PDEs underwent a spectacular development in the last 20 years. For a broad class of equations of mathematical physics, it was proved that under non-degeneracy assumption on the noise acting on the system there is a unique steady state which attracts all other trajectories with an exponential rate. On the other hand, the existing methods are not applicable to a large variety of problems for which the nonlinear term grows at infinity faster than a quadratic function. Recent advances in the theory of inertial manifolds enables one to reduce the infinite-dimensional dynamics to a study of an ordinary differential equation for a number of parabolic PDEs and opens up new possibilities for studying their mixing properties. Our goal is to explore this new direction and to tackle problems not accessible by other means. In particular, we plan to study the complex Ginzburg-Landau equation perturbed by degenerate white-in-time force