5 papers
Heterogeneous diffusion process with power-law nonlinearity
Jorge E. Cardona, Ilya Pavlyukevich
In this paper, we study solutions of the heterogeneous diffusion process with power-law nonlinearity governed by the stochastic differential equation $\mathrm{d}X_t= |X_t|^α\,\math…
Measurable Semigroup Selection of the Heat Flow for Harmonic Maps
Jorge E. Cardona
J.-M. Coron proved in [5] that the global weak solutions of the heat flow from to , starting at non-stationary weakly harmonic maps, are not unique when and $N = S…
Random dynamical system generated by the 3D Navier-Stokes equation with rough transport noise
Jorge Cardona, Martina Hofmanova, Torstein Nilssen +1
We consider the Navier-Stokes system in three dimensions perturbed by a transport noise which is sufficiently smooth in space and rough in time. The existence of a weak solution wa…
Measurable process selection theorem and non-autonomous inclusions
Jorge E. Cardona, Lev Kapitanski
A semi-process is an analog of the semi-flow for non-autonomous differential equations or inclusions. We prove an abstract result on the existence of measurable semi-processes in t…
Semiflow selection and Markov selection theorems
Jorge E. Cardona, Lev Kapitanski
The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup pr…