Time—periodic weak solutions

Weak differentiability of solutions to SDEs with semi-monotone drifts

‎In this work we prove Malliavin differentiability for the solution to an SDE with locally Lipschitz and semi-monotone drift‎. ‎To prove this formula‎, ‎we construct a sequence of SDEs with globally Lipschitz drifts and show that the $p$-moments of their Malliavin derivatives are uniformly bounded‎.

On Weak Solutions of The

Weak Solutions, Renormalized Solutions and Enstrophy Defects in 2d Turbulence

Enstrophy, half the integral of the square of vorticity, plays a role in 2D turbulence theory analogous to that played by kinetic energy in the Kolmogorov theory of 3D turbulence. It is therefore interesting to obtain a description of the way enstrophy is dissipated at high Reynolds number. In this article we explore the notions of viscous and transport enstrophy defect, which model the spatial...

weak differentiability of solutions to sdes with semi-monotone drifts

‎in this work we prove malliavin differentiability for the solution to an sde with locally lipschitz and semi-monotone drift‎. ‎to prove this formula‎, ‎we construct a sequence of sdes with globally lipschitz drifts and show that the $p$-moments of their malliavin derivatives are uniformly bounded‎.

Weak Solutions for a Simple Hyperbolic System

The model studied concerns a simple first-order hyperbolic system. The solutions in which one is most interested have discontinuities which persist for all time, and therefore need to be interpreted as weak solutions. We demonstrate existence and uniqueness for such weak solutions, identifying a canonical ‘exact’ solution which is everywhere defined. The direct method used is guided by the theo...