In this article, we prove that data assimilation by feedback nudging can be achieved for the
three-dimensional quasi-geostrophic equation in a simplified scenario using only large …

An intrinsic property of almost any physical measuring device is that it makes observations
which are slightly blurred in time. The authors consider a nudging-based approach for data …

We discuss the existence of pullback attractors for multivalued dynamical systems on metric
spaces. Such attractors are shown to exist without any assumptions in terms of continuity of …

We construct non-unique weak solutions $\theta\in C_t^ 0C_x^{0-} $ for forced surface quasi-
geostrophic (SQG) equation. This is achieved through a convex integration scheme adapted …

We show the existence of non-unique stationary weak solutions for forced surface quasi-
geostrophic (SQG) equation via a convex integration scheme. The scheme is implemented …

We consider the global attractor of the critical SQG semigroup $ S (t) $ on the scale-invariant
space $ H^ 1 (\mathbb {T}^ 2) $. It was shown in~\cite {CTV13} that this attractor is finite …

The two-dimensional Rayleigh-Bénard problem for a thermomicropolar fluids model is
considered. The existence of suitable weak solutions which may not be unique, and the …

We introduce a determining wavenumber for the surface quasi-geostrophic (SQG) equation
defined for each individual trajectory and then study its dependence on the force. While in …

We construct a determining form for the surface quasi-geostrophic (SQG) equation with
subcritical dissipation. In particular, we show that the global attractor for this equation can be …

We consider the evolution of weak vanishing viscosity solutions to the critically dissipative
surface quasi-geostrophic equation. Due to the possible non-uniqueness of solutions, we …