On Well-posedness of Stochastic Anisotropic p-Laplace Equation Driven by Lévy Noise

Well-posedness of the transport equation by stochastic perturbation

We consider the linear transport equation with a globally Hölder continuous and bounded vector field, with an integrability condition on the divergence. While uniqueness may fail for the deterministic PDE, we prove that a multiplicative stochastic perturbation of Brownian type is enough to render the equation well-posed. This seems to be the first explicit example of partial differential equati...

Stochastic nonlinear Schrödinger equations driven by a fractional noise Well posedness, large deviations and support

We consider stochastic nonlinear Schrödinger equations driven by an additive noise. The noise is fractional in time with Hurst parameter H in (0, 1). It is also colored in space and the space correlation operator is assumed to be nuclear. We study the local well-posedness of the equation. Under adequate assumptions on the initial data, the space correlations of the noise and for some saturated ...

On Stochastic Navier-Stokes Equation Driven by Stationary White Noise

We consider an unbiased approximation of stochastic Navier-Stokes equation driven by spatial white noise. This perturbation is unbiased in that the expectation of a solution of the perturbed equation solves the deterministic Navier-Stokes equation. The nonlinear term can be characterized as the highest stochastic order approximation of the original nonlinear term u∇u. We investigate the analyti...

The well-posedness of an anisotropic parabolic equation based on the partial boundary value condition

Stochastic Liouville equation for particles driven by dichotomous environmental noise.

We analyze the stochastic dynamics of a large population of noninteracting particles driven by a global environmental input in the form of a dichotomous Markov noise process (DMNP). The population density of particle states evolves according to a stochastic Liouville equation with respect to different realizations of the DMNP. We then exploit the connection with previous work on diffusion in ra...