We prove non-uniqueness in law of the three-dimensional magnetohydrodynamics system
that is forced by random noise of an additive and a linear multiplicative type and has viscous …

We consider the momentum formulation of the two-dimensional surface quasi-geostrophic
equations forced by random noise, of both additive and linear multiplicative types. For any …

We prove existence of infinitely many stationary solutions as well as ergodic stationary
solutions for the stochastic Navier-Stokes equations on T 2 d u+ div (u⊗ u) d t+∇ pdt= Δ ud …

We construct solutions to the SQG equation that fail to conserve the Hamiltonian while
having the maximal allowable regularity for this property to hold. This result solves the …

We study the surface quasi-geostrophic equation driven by a generic additive noise process
W. By means of convex integration techniques, we establish existence of weak solutions …

We consider the three-dimensional magnetohydrodynamics system forced by random noise.
First, for smooth solutions in the ideal case, the cross helicity remains invariant while the …

The momentum formulation of the surface quasi-geostrophic equations consists of two
nonlinear terms, besides the pressure term, one of which cannot be written in a divergence …

We explore probabilistic approaches to the deterministic energy equality for the forced
Surface Quasi-Geostrophic (SQG) equation on a torus. First, we prove the zero-noise …

Energy solutions are a probabilistic theory for singular SPDEs with tractable (quasi-)
invariant measures. The prototypical example is the stochastic Burgers/KPZ equation with its …